This paper develops a deep learning-based framework for pricing convertible bonds with path-dependent contractual features, namely downward conversion price reset and issuer call clauses under rolling-window trigger rules, which are widespread in the convertible bond market. We formulate the valuation problem as a path-dependent partial differential equation (PPDE), which explicitly captures the dependence of the convertible bond value on the historical path of the underlying asset and the dynamic evolution of the conversion price. We derive consistent PPDE formulations for three canonical underlying dynamics: geometric Brownian motion (GBM), constant elasticity of variance (CEV) and Heston stochastic volatility. We then construct a discrete-time dynamic programming scheme in which conditional expectations are approximated by neural networks, which remains tractable in such high-dimensional path-dependent setting. Empirical tests on China CITIC Bank Convertible Bond show that our framework produces stable and accurate prices and sensitivity patterns across all model specifications. Three key economic insights emerge: 1. Contractual features dominate underlying dynamics in determining convertible bond values. 2. The call provision decreases convertible bonds prices by truncating upside gains. 3. Counterintuitively, despite improving conversion terms, the downward reset provision further decreases the price of convertible bonds by lowering the effective call threshold and making early redemption more likely. The proposed PPDE-deep learning approach provides an efficient, flexible tool for pricing convertible bonds with complex path-dependent structures.

Filtering problems with jumps in both the signal and the observation have been extensively studied, typically under the assumption that jump times are totally inaccessible. In many applications, however, jump times are known in advance (i.e., predictable), such as scheduled clinical visits, dividend payment dates, or inspection times in engineering systems. Taking predictable jump times as a starting point, we investigate a filtering problem in which both the signal and the observations can exhibit jumps at predictable times. We derive the corresponding Kushner-Stratonovich and Zakai equations, thereby extending classical nonlinear filtering results to a setting with predictable discontinuities. We illustrate the framework on a Kalman filtering model with predictable jumps and on applications to longitudinal clinical studies, such as spinal muscular atrophy (SMA), as well as to machine learning models (neural jump ODEs) and credit risk.

We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian dynamic linear models (DLMs) for asset price series. This represents reduced-form volatility leverage and feedback effects through use of realized volatility proxies in conditional DLMs for prices or returns, coupled with the synthesis of higher frequency data to track and anticipate volatility fluctuations. Analysis is computationally straightforward, extending conjugate-form Bayesian analyses for sequential filtering and model monitoring with simple and direct simulation for forecasting. A main applied setting is equity return forecasting with daily prices and realized volatility from high-frequency, intraday data. Detailed empirical studies of multiple S&P sector ETFs highlight the improvements achievable in asset price forecasting relative to standard models and deliver contextual insights on the nature and practical relevance of volatility leverage and feedback effects. The analytic structure and negligible extra computational cost will enable scaling to higher dimensions for multivariate price series forecasting for decouple/recouple portfolio construction and risk management applications.

In traditional rural societies, where social ties are embedded in physical space, the diffusion of emerging technologies may be amplified through socio-spatial contagion (SSC). Such processes may play a key role in accelerating residential PV adoption in off-grid regions. Yet empirical evidence on SSC in PV adoption remains largely limited to affluent, grid-connected settings, while off-grid regions often lack systematic installation records. To address these gaps, we use a deep learning segmentation model to extract PV installations from a decade-long series of remote sensing imagery across 507 off-grid settlement clusters (hereafter, communities). This enables data-driven spatio-temporal point pattern inference of SSC in data-scarce contexts. SSC is quantified through the range and intensity of clustering of new installations around prior adopters, and the dynamics of these dimensions are linked to adoption outcomes. We found that SSC is nearly ubiquitous, often spanning most of the community's spatial extent, while exhibiting substantial heterogeneity in intensity. Although SSC intensifies over time, its effects remain temporally concentrated, peaking within 1 to 2 years of nearby installations and weakening thereafter. SSC intensity is positively associated with adoption rates in both cross-sectional and temporal analyses. However, the relationship between SSC range and adoption changes over time - in early diffusion phases, adoption growth is associated with range expansion, whereas in later phases it is associated with range contraction. This shift reflects a transition from clustering to consolidation of installations. These findings highlight the potential of seeding interventions to accelerate PV diffusion in off-grid regions.

Electricity price forecasting (EPF) plays a critical role in power system operation and market decision making. While existing review studies have provided valuable insights into forecasting horizons, market mechanisms, and evaluation practices, the rapid adoption of deep learning has introduced increasingly diverse model architectures, output structures, and training objectives that remain insufficiently analyzed in depth. This paper presents a structured review of deep learning methods for EPF in day-ahead, intraday, and balancing markets. Specifically, We introduce a unified taxonomy that decomposes deep learning models into backbone, head, and loss components, providing a consistent evaluation perspective across studies. Using this framework, we analyze recent trends in deep learning components across markets. Our study highlights the shift toward probabilistic, microstructure-centric, and market-aware designs. We further identify key gaps in the literature, including limited attention to intraday and balancing markets and the need for market-specific modeling strategies, thereby helping to consolidate and advance existing review studies.

Cost-of-capital valuation is a well-established approach to the valuation of liabilities and is one of the cornerstones of current regulatory frameworks for the insurance industry. Standard cost-of-capital considerations typically rely on the assumption that the required buffer capital is held in risk-less one-year bonds. The aim of this work is to analyze the effects of allowing investments of the buffer capital in risky assets, e.g.~in a combination of stocks and bonds. In particular, we make precise how the decomposition of the buffer capital into contributions from policyholders and investors varies as the degree of riskiness of the investment increases, and highlight the role of limited liability in the case of heavy-tailed insurance risks. We present a combination of general theoretical results, explicit results for certain stochastic models and numerical results that emphasize the key findings.

Structural change consists of industrial diversification towards more productive, knowledge intensive activities. However, changes in the productive structure bear inherent links with job creation and income distribution. In this paper, we investigate the consequences of structural change, defined in terms of labour shifts towards more complex industries, on employment growth, wage inequality, and functional distribution of income. The analysis is conducted for European countries using data on disaggregated industrial employment shares over the period 2010-2018. First, we identify patterns of industrial specialisation by validating a country-industry industrial employment matrix using a bipartite weighted configuration model (BiWCM). Secondly, we introduce a country-level measure of labour-weighted Fitness, which can be decomposed in such a way as to isolate a component that identifies the movement of labour towards more complex industries, which we define as structural change. Thirdly, we link structural change to i) employment growth, ii) wage inequality, and iii) labour share of the economy. The results indicate that our structural change measure is associated negatively with employment growth. However, it is also associated with lower income inequality. As countries move to more complex industries, they drop the least complex ones, so the (low-paid) jobs in the least complex sectors disappear. Finally, structural change predicts a higher labour ratio of the economy; however, this is likely to be due to the increase in salaries rather than by job creation.

Recent empirical evidence shows that investments in ICT disproportionately improve the performance of larger firms versus smaller ones. However, ICT may not be all alike, as they differ in their impact on firms' organisational structure. We investigate the effect of the use of cloud services on the long run size growth rate of French firms. We find that cloud services positively impact firms' growth rates, with smaller firms experiencing more significant benefits compared to larger firms. Our findings suggest cloud technologies help reduce barriers to digitalisation, which affect especially smaller firms. By lowering these barriers, cloud adoption enhances scalability and unlocks untapped growth potential.

Financial and gambling markets are ostensibly similar and hence strategies from one could potentially be applied to the other. Financial markets have been extensively studied, resulting in numerous theorems and models, while gambling markets have received comparatively less attention and remain relatively undocumented. This study conducts a comprehensive comparison of both markets, focusing on trading rather than regulation. Five key aspects are examined: platform, product, procedure, participant and strategy. The findings reveal numerous similarities between these two markets. Financial exchanges resemble online betting platforms, such as Betfair, and some financial products, including stocks and options, share speculative traits with sports betting. We examine whether well-established models and strategies from financial markets could be applied to the gambling industry, which lacks comparable frameworks. For example, statistical arbitrage from financial markets has been effectively applied to gambling markets, particularly in peer-to-peer betting exchanges, where bettors exploit odds discrepancies for risk-free profits using quantitative models. Therefore, exploring the strategies and approaches used in both markets could lead to new opportunities for innovation and optimization in trading and betting activities.

This paper studies the topic of cost-efficiency in incomplete markets. A payoff is called cost-efficient if it achieves a given probability distribution at some given investment horizon with a minimum initial budget. Extensive literature exists for the case of a complete financial market. We show how the problem can be extended to incomplete markets and how the main results from the theory of complete markets still hold in adapted form. In particular, we find that in incomplete markets, the optimal portfolio choice for non-decreasing preferences that are diversification-loving (a notion introduced in this paper) must be "perfectly" cost-efficient. This notion of perfect cost-efficiency is shown to be equivalent to the fact that the payoff can be rationalized, i.e., it is the solution to an expected utility problem.

The geometric approach to financial markets with proportional transaction cost prescribes to imbed a specific model (of stock market, of currency market etc.), usually given in a parametric form, into a natural framework defined by the two random processes, S and K. The first one, d-dimensional, models the price evolution of basic securities while the second one, cone-valued, describes the evolution of the solvency set. It happened that the fundamental questions -- no-arbitrage criteria, hedging problems, portfolio optimization -- can be studied in this general setting opening the door to set-valued techniques. In this note we explore, in such a general framework, the stochastic Mayer control problem, consisting in the maximization of the expected utility of the portfolio terminal wealth. We get results on continuity of the optimal value and the optimal control under price approximations in a general multi-asset framework described by the geometric formalism.

Herding -- where agents align their behaviors and act collectively -- is a central driver of market fragility and systemic risk. Existing approaches to quantify herding rely on price-correlation statistics, which inherently lag because they only detect coordination after it has already moved realised returns. We propose GeomHerd, a forward-looking geometric framework that bypasses this observability lag by quantifying coordination directly on upstream agent-interaction graphs. To generate these graphs, we treat a heterogeneous LLM-driven multi-agent simulator -- each financial trader instantiated by a persona-conditioned LLM call -- as a forecastable world, and evaluate the geometric pipeline on the Cividino--Sornette continuous-spin agent-based substrate as our headline financial testbed. By tracking the discrete Ollivier--Ricci curvature of these action graphs, GeomHerd captures the structural topology of emerging coordination. Theoretically, we establish a mean-field bridge mapping our graph-theoretic metric to CSAD, the classical macroscopic herding statistic, linking GeomHerd to downstream price-dispersion measurement. Empirically, GeomHerd anticipates herding long before aggregate market baselines: on the continuous-spin substrate, our primary detector fires a median of 272 steps before order-parameter onset; a contagion detector ($β_{-}$) recalls 65% of critical trajectories 318 steps early; and on co-firing trajectories the agent-graph signal precedes price-correlation-graph baselines by 40 steps. As a complementary indicator, the effective vocabulary of agent actions contracts during cascades. The geometric signature transfers out-of-domain to the Vicsek self-driven-particle model, and a curvature-conditioned forecasting head reduces cascade-window log-return MAE over detector-conditioned and price-only baselines.

Prediction markets cannot exist without market makers, arbitrageurs, and other non-retail liquidity providers, yet the supply-side microstructure of Polymarket-class venues has not been characterized at on-chain pseudonymous-address scale. This paper studies non-retail participation on Polymarket using an empirical run on the PMXT v2 archive over 2026-04-21 through 2026-04-27 (13,356,931 OrderFilled events; 77,204 addresses with five+ fills; 43,116 markets). We report three findings. First, Polymarket's off-chain CLOB architecture renders address-level quote-lifecycle attribution permanently unavailable: OrderPlaced and OrderCancelled events are off-chain and absent from public archives, so quote-intensity, two-sided-ratio, and posted-spread features cannot be built at address level. We document this as a structural validity-gate failure (G-QUOTE-LIFE universal fail) and restrict analysis to a six-feature fill-side vector. Second, density-based clustering (DBSCAN, fifteen sensitivity configurations) on the fill-side vector produces a single dense cluster with zero noise: fill-side behavior in the empirical window is uni-modal under the six-feature vector, contradicting the pre-registered hypothesis of four-to-five separable archetypes. Third, robust retail vs non-retail separation is achievable through clustering-independent feature-tier stratification: whale-tier, high-frequency-operator, and power-trader tiers jointly hold 81.4% of total notional across 12.6% of addresses. Address-level market-making and liquidity-provision claims are withdrawn per the G-QUOTE-LIFE failure; spoof-by-non-fill manipulation detection is downgraded to market-level book diagnostics. A privacy-respecting derived-dataset deposit accompanies the paper as Bundle 3 of the PMXT family. Fourth paper in a four-paper programme on event-linked perpetuals and leveraged prediction-market microstructure.

This paper constructs and validates a composite day-classification system for Micro E-Mini Nasdaq 100 futures (MNQ) using three pre-market observable conditions: first-30-minute return magnitude, overnight gap magnitude, and abnormal opening-bar volume relative to a rolling baseline. Using 947 regular trading days of five-minute data from 2021-2025, we find that classifier-positive days exhibit statistically distinct intraday behavior, including directional morning drift followed by systematic late-session reversal. Despite these descriptive characteristics, all tested directional trading strategies fail institutional validation standards after transaction costs and multi-year consistency requirements are applied. The highest-performing configuration achieves T = 1.46 and mean net +7.80 points but fails year-stability criteria. The primary contribution is the validation of the Volatility-Volume-Gap (VVG) classifier as a descriptive regime-identification framework and the documentation of failed attempts to convert these statistical patterns into deployable trading signals under realistic execution constraints.

We formulate and solve stochastic control problems that model the core yield-generating strategy of the Ethena protocol, a decentralized finance (DeFi) stablecoin that earns yield by combining a long position in staked Ethereum (stETH) with an equal-sized short position in ETH perpetual futures. The combined position is delta-neutral with respect to the ETH spot price, yet earns carry from two sources: staking rewards on the stETH leg, and funding-rate payments received from long perpetual holders when the perpetual trades at a premium to spot. A key feature of our model is that the control -- the rate of simultaneously buying stETH and shorting the perpetual -- exerts two distinct types of price impact. \textit{Permanent} impact shifts the mid-market prices of both legs, compressing the basis and permanently eroding future funding income. \textit{Temporary} impact reflects execution slippage on each leg. We study both an infinite-horizon discounted problem and a finite-horizon problem in which the protocol maximizes total wealth up to a fixed date $T$, subject to a terminal cost for liquidating any remaining position. In both cases the optimal control is obtained explicitly.

Risk governance is not only about identifying and measuring adverse states of the world. It also asks when an institution is entitled to rely on a risk claim. This paper introduces modal epistemic tools for that second layer of QRM. For a risk proposition $p$, $Kp$ denotes assurance-grade endorsement for certification, audit reliance, board sign-off, or regulatory reporting. By contrast, $Bp$ denotes working commitment: a disciplined action-guiding stance under incomplete assurance. The framework distinguishes object-level risk claims from stances toward them. It develops crisp and fuzzy modal semantics for assurance, working commitment, live possibility, non-exclusion, hesitation, and epistemic inconsistency. The central diagnostics are \[ p\wedge\neg Kp \qquad\text{and}\qquad p\wedge\neg Bp, \] which identify cases in which a risk is present but lacks the relevant stance. Thus QRM should model not only hazards and losses, but also evidential incompleteness, model risk, validation gaps, and failures of escalation. Two governance principles motivate the analysis. The Risk Management Principle says that if $p$ is a risk, then the absence of the relevant stance, $p\wedge\neg Mp$, is itself risk-relevant. The Risk Reach Principle says that real and decision-relevant risks should be reachable by the appropriate stance. Their unrestricted combination creates Moorean and Fitch-style collapse pressure: treating $p\wedge\neg Kp$ or $p\wedge\neg Bp$ as ordinary targets of the same stance whose absence they record undermines the diagnostic. The response is architectural. Object-level risk claims should be separated from meta-level epistemic diagnostics. The latter should be governed through an audit layer that records and controls epistemic gaps. This preserves action and precaution without collapsing risk governance into institutional omniscience.

We show that under mild assumptions, the total value of information to informed traders in the market can be measured by the covariance between price changes and order flow. This covariance captures noise trader losses, which equal informed trader gains when market making is competitive. We estimate the value of information using high frequency data on US equities at about $3.5 million per year for the average stock. The aggregate value of information is about 0.04% of market cap, which is considerably lower than the 0.67% in fees investors pay each year searching for superior returns (French 2008). We discuss potential resolutions for these puzzling findings.

We introduce a transport cohomological framework for categorical filtrations. Given a contravariant filtration $F:\mathcal T^{op}\to\mathbf{Prob}$ on a small category \(\mathcal T\), conditional expectation induces transport operators between local probabilistic states. Using the simplicial structure of the nerve \(N_\bullet(\mathcal T)\), we construct simplex-local cochain complexes associated with parametrized simplices and study their transport cohomology. The resulting framework naturally produces loop effects and holonomy structures. In particular, transport around closed simplicial histories may generate nontrivial probabilistic distortions, even when the initial and terminal objects coincide. The associated holonomy operators encode global transport effects between probabilistic states and detect obstructions generated by loop transport. This leads to the notion of homological arbitrage, understood as a global transport phenomenon emerging from probabilistic distortion along loops. From this viewpoint, the essential source of loop effects is the probabilistic distortion generated by transport around closed simplicial histories. The present framework is structurally analogous to parallel transport and holonomy in differential geometry, providing a geometric viewpoint on categorical filtrations and probabilistic transport structures.

We identify the measurable absorbing obstruction to uniqueness of invariant probability measures for a Markov kernel. Ordinary absorbing decompositions obstruct global irreducibility and recurrence, but not necessarily uniqueness: an absorbing component may have full mass for no invariant probability. We prove that a Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition, namely two disjoint absorbing sets, each having full mass for an invariant probability. The proof uses only the Jordan decomposition of the difference of two invariant probabilities.

Copula-based Conditional Value at Risk (CCVaR) is defined as an alternative version of the classical Conditional Value at Risk (CVaR) for multivariate random vectors intended to be real-valued. We aim to generalize CCVaR to several dimensions (d>=2) when the dependence structure is given by an Archimedean copula. While previous research focused on the bivariate case, leaving the multivariate version unexplored, an almost closed-form expression for CCVaR under an Archimedean copula is derived. The conditions under which this risk measure satisfies coherence are then examined. Finally, numerical experiments based on real data are conducted to estimate CCVaR, and the results are compared with classical measures of Value at Risk (VaR) and Conditional Value at Risk (CVaR).

This paper investigates optimal investment and insurance strategies under a mean-variance criterion with path-dependent effects. We use a rough volatility model and a Hawkes process with a power kernel to capture the path dependence of the market. By adding auxiliary state variables, we degenerate a non-Markovian problem to a Markovian problem. Next, an explicit solution is derived for a path-dependent extended Hamilton-Jacobi-Bellman (HJB) equation. Then, we derive the explicit solutions of the problem by extending the Functional Ito formula for fractional Brownian motion to the general path-dependent processes, which includes the Hawkes process. In addition, we use earthquake data from Sichuan Province, China, to estimate parameters for the Hawkes process. Our numerical results show that the individual becomes more risk-averse in trading when stock volatility is rough, while more risk-seeking when considering catastrophic shocks. Moreover, an individual's demand for catastrophe insurance increases with path-dependent effects. Our findings indicate that ignoring the path-dependent effect would lead to a significant underinsurance phenomenon and highlight the importance of the path-dependent effect in the catastrophe insurance pricing.

Do high-return fields of study provide greater protection in labor market during crises? I construct pre-pandemic premia for major technical fields in India and examine whether workers in higher field-premium fields experience resilient labor market outcomes during COVID-19. Using a difference-in-difference with continuous treatment design, I find that field-premium advantages did not emerge immediately at the onset of the pandemic but through gradual adjustment during later phases.

This paper investigates the impact of posterior drift on out-of-sample forecasting accuracy in overparametrized machine learning models. We document the loss in performance when the loadings of the data generating process change between the training and testing samples. This matters crucially in settings in which regime changes are likely to occur, for instance, in financial markets. Applied to equity premium forecasting, our results underline the sensitivity of a market timing strategy to sub-periods and to the bandwidth parameters that control the complexity of the model. For the average investor, we find that focusing on holding periods of 15 years can generate very heterogeneous returns, especially for small bandwidths. Large bandwidths yield much more consistent outcomes, but are far less appealing from a risk-adjusted return standpoint. All in all, our findings tend to recommend cautiousness when resorting to large linear models for stock market predictions.

Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth $W_t$ quantifies the evidence against the null hypothesis after $t$ rounds, and the null can be rejected at level $α$ whenever $W_t \geq 1/α$. A key assumption permeating the literature is that one cannot bet more money than they currently have (the wealth must stay nonnegative). In this work, we examine the consequences of allowing the bettor to borrow money in each round (for example after going bankrupt). Specifically, we ask how the threshold of $1/α$ must be accordingly adjusted to retain the desired level $α$. Our findings are twofold. First, if the new rejection rule is $W_t \geq g(α,L_t)$ where $L_t$ is the total liability at time $t$, then we show that $g(α,0)>1/α$ if $g(α,L_t)<\infty$ for any $L_t > 0$; in words, we must pay for the possibility of borrowing, even if in fact we do not borrow. Second, and in contrast to the first, if one employs a path dependent threshold $h(α,W_0,L_1,\dots,W_{t-1},L_t)$, that is a function of past leverage ratios, then there is in fact no extra price to pay for the possibility of borrowing.