数理金融

Herding behavior has become a familiar phenomenon to investors, with potential dangers of both undervaluing and overvaluing assets, while also threatening market stability. This study contributes to the literature on herding behavior by…

In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling…

The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the…

We study and solve the worst-case optimal portfolio problem as pioneered by Korn and Wilmott (2002) of an investor with logarithmic preferences facing the possibility of a market crash with stochastic market coefficients by enhancing the…

We consider the joint SPX-VIX calibration within a general class of Gaussian polynomial volatility models in which the volatility of the SPX is assumed to be a polynomial function of a Gaussian Volterra process defined as a stochastic…

This article analytically characterizes the impermanent loss for automatic market makers in decentralized exchanges such as Uniswap or Balancer (CPMM). We present a theoretical static replication formula for the pool value using a…

This paper investigates robust stochastic differential games among insurers under model uncertainty and stochastic volatility. The surplus processes of ambiguity-averse insurers (AAIs) are characterized by drifted Brownian motion with both…

This paper studies the robust reinsurance and investment games for competitive insurers. Model uncertainty is characterized by a class of equivalent probability measures. Each insurer is concerned with relative performance under the…

While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by…

Fourier pricing methods such as the Carr-Madan formula or the COS method are classic tools for pricing European options for advanced models such as the Heston model. These methods require tuning parameters such as a damping factor, a…

We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no-arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs.…

Automated market makers are a popular mechanism used on decentralized exchange, through which users trade assets with each other directly and automatically through a liquidity pool and a fixed pricing function. The liquidity provider…

This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…

We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the…

Over the past 60 years, there has been a gradual increase in the volatility of daily returns for the S&P 500 Index. Hypothetically, suppose that market forces determine daily volatility such that a daily leveraged S&P 500 fund cannot…

This article presents a mathematical model of dynamic pricing for real estate (RE) that incorporates multiple pricing groups, thereby expanding the capabilities of existing models. The developed model solves the problem of maximizing…

We address the problem of asset pricing in a market where there is no risky asset. Previous work developed a theoretical model for a shadow riskless rate (SRR) for such a market in terms of the drift component of the state-price deflator…

This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents based on the mean field game theory. In the model, we incorporate habit formation in consumption preferences, which has been…

This paper proposes a new approach using the stochastic projected gradient method and Malliavin calculus for optimal reinsurance and investment strategies. Unlike traditional methodologies, we aim to optimize static investment and…

We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…