For independent multi-outcome events under multiplicative parlay pricing, we give a short exact proof of the optimal Kelly strategy using the implicit-cash viewpoint. The proof is entirely eventwise. One first solves each event in isolation. The full simultaneous optimizer over the entire menu of singles, doubles, triples, and higher parlays is then obtained by taking the outer product of the one-event Kelly strategies. Equivalently, the optimal terminal wealth factorizes across events. This yields an immediate active-leg criterion: a parlay is active if and only if each of its legs is active in the corresponding one-event problem. The result recovers, in a more transparent state-price form, the log-utility equivalence between simultaneous multibetting and sequential Kelly betting. We then study what is lost when one forbids parlays and allows only singles. In a low-edge regime and on a fixed active support, the exact parlay optimizer supplies the natural reference point. The singles-only problem is a first-order truncation of the factorized wealth formula. A perturbative expansion shows that the growth-rate loss from forbidding parlays is $\OO(\eps^4)$, while the optimal singles stakes deviate from the isolated one-event Kelly stakes only at cubic order. This yields a clean explanation of Whitrow's empirical near-proportionality phenomenon: the simultaneous singles-only optimizer is obtained from the isolated eventwise optimizer by an event-specific cubic shrinkage, so the portfolios agree through second order and differ only by a small blockwise drag.

Political discourse attributes the pressure on European welfare systems to foreign nationals. Yet projections of service demand rarely disaggregate service demand by citizenship status. We develop a structural demographic model and project healthcare, education, and housing demand in Austria through 2050, disaggregated by citizenship status and regions across migration scenarios. We find that migration, ageing, and fertility shape each sector differently. In healthcare, the ageing of Austrian nationals contributes 4.7 times more to demand growth than immigration, with the most acute pressures in rural, low-migration regions. In housing, migration accounts for the entire net growth in demand, concentrated in metropolitan hubs. In education, aggregate demand contracts regardless of migration assumptions, whereas future needs are driven more by the births of foreigners in Austria than by new arrivals. Foreign nationals consume services in proportion to their demographic weight, with deviations explained by age structure rather than over-utilisation. These results show that the drivers of service demand are sector-specific: migration restrictions could ease housing pressure, but would not address ageing-driven healthcare demand and may accelerate contraction in the education system.

In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the theoretical analysis of this general model, we focus on the rBergomi and rHeston models and their calibration to market data of vanilla futures options on WTI Crude Oil. Finally, numerical results illustrate the performance of the proposed rough volatility models for commodities pricing.

This article proposes a new class of risk-sharing rules by exploring the relationship between capital allocation and risk sharing. While the former is concerned with ex-ante allocating capitals to different lines of business within a corporation based on the relationship among the individual risks, often also through the aggregate risk, the latter is an arrangement which collects risks from and allocates them to, also ex-ante, a group of participants. Drawing on this analogy, we introduce a novel idea of inducing risk-sharing rules by randomizing existing capital allocation principles. Such an approach derives new risk-sharing rules complementing known results in the literature, which were largely based on economic principles and Pareto optimality.

Blockchain technology introduces asset types and custody mechanisms that fundamentally break traditional financial auditing paradigms. This paper presents an autoethnographic analysis of cryptoasset auditing challenges, build on top of prior research on a comprehensive framework addressing existence, ownership, valuation, and internal control verification. Drawing from lived experience implementing blockchain systems as an engineer, smart contract auditor, and CTO of a publicly traded cryptoasset firm, we demonstrate how autoethnographic methodology becomes necessary for understanding technical complexities that external analysis cannot capture. Through detailed examination of token airdrops, multi-signature smart contracts, and real-time on-chain reporting, we provide experimental approaches and common scenarios that auditing firms can analyze to address blockchain innovations currently considered technically insurmountable.

We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing high-dimensional price surfaces in tensor-train (TT) form using TT-cross approximation, constructing the surrogate directly from black-box price evaluations without materializing the full training tensor. For inference, we use a Laplacian kernel and derive TT representations of the kernel matrix and its closed-form inverse in the noise-free setting, enabling TT-based Gaussian process regression without dense matrix factorization or iterative linear solves. We found that hyperparameter optimization consistently favors a large kernel length-scale and show that in this regime the GPR predictor reduces to multilinear interpolation for off-grid inputs; we also derive a low-rank TT representation for this limit. We evaluate the approach on five-asset basket options over an eight dimensional parameter space (asset spot levels, strike, interest rate, and time to maturity). For European geometric basket puts, the tensor surrogate achieves lower test error at shorter training times than standard GPR by scaling to substantially larger effective training sets. For American arithmetic basket puts trained on LSMC data, the surrogate exhibits more favorable scaling with training-set size while providing millisecond-level evaluation per query, with overall runtime dominated by data generation.

We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the semi-structured model provides modest but consistent gains in discrimination across the earliest prediction spans, while maintaining similar Brier scores. Adding macroeconomic indicators provides limited incremental benefit in this out-of-time evaluation and does not materially change the estimated borrower-, loan-, or duration-driven effects. Overall, semi-structured multi-state modelling offers a practical compromise between transparent effect estimates and flexible pattern learning, with potential applications beyond credit-transition forecasting.

We present a strictly monotone, provably convergent two-dimensional (2D) integration method for multi-period mean-conditional value-at-risk (mean-CVaR) reward-risk stochastic control in models whose one-step increment law is specified via a closed-form characteristic function (CF). When the transition density is unavailable in closed form, we learn a nonnegative, normalized 2D transition kernel in Fourier space using a simplex-constrained Gaussian-mixture parameterization, and discretize the resulting convolution integrals with composite quadrature rules with nonnegative weights to guarantee monotonicity. The scheme is implemented efficiently using 2D fast Fourier transforms. Under mild Fourier-tail decay assumptions on the CF, we derive Fourier-domain $L_2$ kernel-approximation and truncation error estimates and translate them into real-space bounds that are used to establish $\ell_\infty$-stability, consistency, and pointwise convergence as the discretization and kernel-approximation parameters vanish. Numerical experiments for a fully coupled 2D jump--diffusion model in a multi-period portfolio optimization setting illustrate robustness and accuracy.

Transfer-based anti-money laundering (AML) systems monitor token flows through transaction-graph abstractions, implicitly assuming that economically meaningful value migration is sufficiently encoded in transfer-layer connectivity. In this paper, we demonstrate that this assumption, the bedrock of current industrial forensics, fundamentally collapses in composable smart-contract ecosystems. We formalize two structural mechanisms that undermine the completeness of transfer-layer attribution. First, we introduce Principal-Execution-Beneficiary (PEB) separation, where intent originators, transaction executors (e.g., MEV searchers), and ultimate beneficiaries are functionally decoupled. Second, we formalize state-mediated value migration, where economic coupling is enforced through invariant-driven contract state transitions (e.g., AMM reserve rebalancing) rather than explicit transfer continuity. Through a real-world case study of role-separated limit order execution and a constructive cross-pool arbitrage model, we prove that these mechanisms render transfer-layer observation neither attribution-complete nor causally closed. We further argue that simply expanding transfer-layer tracing capabilities fails to resolve the underlying attribution ambiguity inherent in structurally decoupled execution. Under modular composition and open participation markets, these mechanisms are structurally generative, implying that heuristic-based flow tracing has reached a formal observational boundary. We advocate for a paradigm shift toward AML based on execution semantics, focusing on the restitution of economic causality from atomic execution logic and state invariants rather than static graph connectivity.

Although climate and nature related scenario analysis is increasingly important in finance, operational implementations remain limited for translating long horizon environmental scenarios into counterparty credit risk measures used in pricing and regulatory capital. We propose an environmental valuation adjustment framework for CVA with three components: (i) a scenario to credit translation that maps environmental scenario drivers into hazard rates; (ii) nature specific tail generators that quantify model risk in scenario generation; and (iii) a distributionally robust wrong way risk bound based on Kullback Leibler (KL) divergence. We compute climate CVAs using transition scenarios and nature CVAs using biodiversity indicators. Our results show that nature CVAs can vary materially across alternative ecosystem generators, highlighting an additional source of model uncertainty.

A common practice in empirical finance is to construct calendar-aligned panels that implicitly treat all instruments as having existed for the full observation period. When securities with different listing histories are combined without explicit coverage constraints, price histories can be inadvertently extended before valid trading ever began. This paper formalizes this problem and proposes a coverage-aware structuring framework built around instrument-level observation windows encoded through structured metadata and an availability matrix. Applied to end-of-day data from the Dhaka Stock Exchange spanning October 2012 to January 2026 and covering 486 instruments, the framework reveals substantial distortions from naive temporal alignment. ARIMA-based experiments establish the mechanism through which padded observations corrupt return dynamics, and volatility analysis across 53 instruments shows that forward-filling alone suppresses return volatility by roughly 20% on average, with GARCH unconditional variance distortions exceeding 26% in over 90% of instruments - a lower bound, as backward extension to the panel start produces 36.6% suppression and causes GARCH non-convergence in 41% of instruments. The distortion affects any method requiring calendar alignment of heterogeneous histories, including dynamic time warping, covariance-based portfolio construction, factor model regression, and temporal foundation model fine-tuning. Although demonstrated on financial data, the framework applies to any panel combining entities with heterogeneous entry dates, including sensor networks, clinical cohorts, and country-level economic panels. Listing coverage is not a minor preprocessing detail but a first-order variable in panel construction.

Rendering fair prices for financial, credit, and insurance products is of ethical and regulatory interest. In many jurisdictions, discriminatory covariates, such as gender and ethnicity, are prohibited from use in pricing such instruments. In this work, we propose a discrimination-insensitive pricing framework, where we require the pricing principle to be insensitive to the (exogenously determined) protected covariates, that is the sensitivity of the pricing principle to the protected covariate is zero. We formulate and solve the optimisation problem that finds the nearest (in Kullback-Leibler (KL) divergence) "pricing" measure to the real world probability, such that under this pricing measure the principle is discrimination-insensitive. We call the solution the discrimination-insensitive measure and provide conditions for its existence and uniqueness. In situations when there are more than one protected covariates, the discrimination-insensitive pricing measure might not exist, and we propose a two-step procedure. First, for each protected covariate separately, we find the measure under which the pricing principle becomes insensitivity to that covariate. Second we reconcile these measures through a constrained barycentre model. We provide a close-form solution to this problem and give conditions for existence and uniqueness of the constrained barycentre pricing measure. As an intermediary result, we prove the representation, existence, and uniqueness of the KL barycentre of general probability measures, which may be of independent interest. Finally, in a numerical illustration, we compare our discrimination-insensitive premia and the constrained barycentre pricing measure with recently proposed fair premia from the actuarial literature.

Dependence among multiple lifetimes is a key factor for pricing and evaluating the risk of joint life insurance products. The dependence structure can be exposed to model uncertainty when available data and information are limited. We address robust pricing and risk evaluation of joint life insurance products against dependence uncertainty between two lifetimes. We first show that, for some class of standard contracts, the risk evaluation based on a distortion risk measure is monotone with respect to the concordance order of the underlying copula. Based on this monotonicity, we then study the most conservative and anti-conservative risk evaluations for this class of contracts. We prove that the bounds for the mean, Value-at-Risk and Expected Shortfall are computed by combinations of linear programs when the uncertainty set is defined by a norm-ball centered around a reference copula. Our numerical analysis reveals that the sensitivity of the risk evaluation against the choice of the copula differs depending on the risk measure and the type of the contract, and our proposed bounds can improve the existing bounds based on the available information.

The prediction of foreign exchange rates, such as the US Dollar (USD) to Bangladeshi Taka (BDT), plays a pivotal role in global financial markets, influencing trade, investments, and economic stability. This study leverages historical USD/BDT exchange rate data from 2018 to 2023, sourced from Yahoo Finance, to develop advanced machine learning models for accurate forecasting. A Long Short-Term Memory (LSTM) neural network is employed, achieving an exceptional accuracy of 99.449%, a Root Mean Square Error (RMSE) of 0.9858, and a test loss of 0.8523, significantly outperforming traditional methods like ARIMA (RMSE 1.342). Additionally, a Gradient Boosting Classifier (GBC) is applied for directional prediction, with backtesting on a $10,000 initial capital revealing a 40.82% profitable trade rate, though resulting in a net loss of $20,653.25 over 49 trades. The study analyzes historical trends, showing a decline in BDT/USD rates from 0.012 to 0.009, and incorporates normalized daily returns to capture volatility. These findings highlight the potential of deep learning in forex forecasting, offering traders and policymakers robust tools to mitigate risks. Future work could integrate sentiment analysis and real-time economic indicators to further enhance model adaptability in volatile markets.

Participants in online experiments often enroll over time, which can compromise sample representativeness due to temporal shifts in covariates. This issue is particularly critical in A/B tests, online controlled experiments extensively used to evaluate product updates, since these tests are cost-sensitive and typically short in duration. We propose a novel framework that dynamically assesses sample representativeness by dividing the ongoing sampling process into three stages. We then develop stage-specific estimators for Population Average Treatment Effects (PATE), ensuring that experimental results remain generalizable across varying experiment durations. Leveraging survival analysis, we develop a heuristic function that identifies these stages without requiring prior knowledge of population or sample characteristics, thereby keeping implementation costs low. Our approach bridges the gap between experimental findings and real-world applicability, enabling product decisions to be based on evidence that accurately represents the broader target population. We validate the effectiveness of our framework on three levels: (1) through a real-world online experiment conducted on WeChat; (2) via a synthetic experiment; and (3) by applying it to 600 A/B tests on WeChat in a platform-wide application. Additionally, we provide practical guidelines for practitioners to implement our method in real-world settings.

In European day-ahead electricity markets, carbon allowance costs passed through by marginal fossil plants raise consumer expenditure and generate inframarginal rents for non-emitting generators. We propose a settlement modification: when the zonal day-ahead price exceeds a threshold, non-emitting generation is remunerated at the clearing price minus a fixed CO2 proxy deduction, while all other units continue to receive the uniform price. The mechanism thus reallocates a part of the inframarginal rents to consumers. Using hourly data we estimate static average expenditure reductions of about 8.5% in Austria and 4.7% in Germany in 2025. We discuss bidding incentives around the threshold, interactions with Contracts for Difference, implementation in coupled bidding zones, and a gas-cost variant for the 2022 energy crisis.

A growing literature documents how religious institutions shape behavior through social influence, but less is known about what happens when religious movements gain political power and use the tools of government to advance their agenda. We use a regression discontinuity design on close mayoral elections in Brazil to show that mayors from parties institutionally tied to Pentecostal denominations increase teenage fertility 3 per 1,000 higher (a 40% increase). This effect appears for cohorts exposed to middle school during the administration. Consistent with a school-based mechanism, we find that the likelihood that municipal schools offer sexual education programs falls by 12.5 percentage points, with no changes in state schools outside mayoral control. We also find elevated STD rates, and higher middle school dropout rates, while slightly older cohorts show no effects. Results are not explained by changes in contraceptive availability in public clinics, pointing to sexual education as the primary mechanism. We also find no effects from other right-wing parties, indicating the importance of institutional links to Pentecostal parties.

In many search markets, advance interim contracts include an explicit right to renege, granting one party the option to switch to more attractive matches that emerge later in the search process. This paper studies the design and welfare implications of such interim contracts, leveraging novel data from a brokerage firm in the trucking industry. The broker allocates advance shipment contracts to carriers through a dynamic auction mechanism and penalizes cancellations through a reputational mechanism. I develop a theoretical model linking the carrier's bidding problem to the firm's cancellation penalties through a dynamic job-search problem and structurally estimate the model from rich data on bids and cancellations. In counterfactual simulations, I show that the firm is incentivized to lower cancellation penalties as the option value of the right to renege is priced into carrier bids. The results rationalize the large degree of contractual flexibility observed in the trucking industry as an efficient market outcome rather than one constrained by limited enforcement.