Quantitative Finance
This review summarizes the historical development of probability measures in asset pricing, from early mathematical finance and state price theory to risk-neutral valuation, martingale measures, forward measures, stochastic discount…
We extract four geometric observables -- Berry Phase Rate, Spectral Entropy, Reduced State Purity, and Hamiltonian Sensitivity -- from a learned spectral embedding of equity-index returns and evaluate them as regime-shift detectors against…
This paper investigates how large language models (LLMs) form and express investor risk profiles, a critical component of retail investment advising. We examine three LLMs (GPT, Gemini, and Llama) and assess their responses to a…
This study introduces a benchmark framework for evaluating the financial decision-making capabilities of large language models (LLMs) through portfolio optimization problems with mathematically explicit solutions. Unlike existing financial…
The rapid advancement of Large Language Models (LLMs) has led to a surge of financial benchmarks, evolving from static knowledge evaluation toward interactive trading simulations. However, existing frameworks for evaluating real-time…
In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic…
Transition-related financial markets are increasingly exposed to abrupt repricing episodes, elevated volatility, and heterogeneous macro-financial shocks. Under such conditions, conventional Gaussian-linear forecasting frameworks may…
Ownership concentration is not a scalar. For a normalized investor-stock matrix $A$, it has three irreducible layers: concentration across investors, concentration across stocks, and dependence in the joint assignment of investors to…
We propose a foundational runtime actuarial layer for autonomous AI agents in which every side-effect-bearing action carries a time-consistent, counterfactual risk toll computed against a contractually fixed safe default, inside an explicit…
Motivated by the emergence of local groundwater exchanges, we construct and analyze stochastic models of dynamic groundwater markets. Our primary focus is endogenizing the price formation and groundwater pumping strategies in a closed…
Deep learning offers new tools for portfolio optimization. We present an end-to-end framework that directly learns portfolio weights by combining Long Short-Term Memory (LSTM) networks to model temporal patterns, Graph Attention Networks…
We study the problem of hedging unit linked life insurance policies whose benefits depend on an investment fund that incorporates environmental criteria in its selection process. Offering these products poses two key challenges:…
An empirical analysis, suggested by optimal Merton dynamics, reveals some unexpected features of asset volumes. These features are connected to traders' belief and risk aversion. This paper proposes a trading strategy model in the optimal…
This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a…
Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, L\'evy copulas and zero-mixed models, often face practical difficulties in simulation and…
This paper examines the valuation and hedging of standard equity protection swap (EPS) products proposed by Xu et al.. To account for financial crises and counterparty default risk, we develop pricing frameworks based on Merton's…
Partially convertible economies face a market-design problem: trade integration, cross-border investment, and domestic balance-sheet exposure increase the demand for currency hedging before full financial integration is complete. China…
We study a finite-inventory risk-sensitive market making problem in which a dealer controls bid and ask quotes, faces Brownian midprice risk, and receives liquidity-taking orders through point processes with quote-dependent intensities. The…
This paper studies the joint role of long-memory dynamics,rough-volatility behavior, and persistence-based forecasting features in equity volatility modeling. We combine semiparametric long-memory estimation, rough-volatility diagnostics,…
This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit…