在内生定价下的效用最大化

Indifference pricing for Contingent Claims: Large Deviations Effects

We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors. We make connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where in the $n^{th}$ market, the claim $B_n$ admits the decomposition $B_n = D_n+Y_n$. Here, $D_n$ is replicable by trading in the underlying assets $S_n$, but $Y_n$ is independent of $S_n$. Under broad conditions, we may assume that $Y_n$ vanishes in accordance with a large deviations principle as $n$ grows. In…

A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of agents are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the o…

含指数效用的均值场均衡资产定价模型

Mean Field Equilibrium Asset Pricing Models With Exponential Utility

本文提出基于均值场博弈理论的不完全市场资产定价模型，研究异质投资者的均衡风险溢价，通过均值场反向随机微分方程解决最优投资问题，并引入指数二次高斯方法获得半解析解。

Arbitrage, hedging and utility maximization using semi-static trading strategies with American options

We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (FTAP). Using the FTAP, we get the dualities for the hedging prices of European and American options. Based on the hedging dualities, we also get the duality for the utility maximiz…

Asset Pricing with General Transaction Costs: Theory and Numerics

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the sco…

内生碳价格下绿色技术采纳的平稳均衡模型

A Stationary Equilibrium Model of Green Technology Adoption with Endogenous Carbon Price

本文构建了一个内生碳价格的竞争性行业平稳均衡模型，研究企业在不可逆减排投资下的绿色技术采纳行为，并结合布朗技术冲击案例分析了碳定价、补贴与税收政策对投资时机的影响及福利最优排放目标的作用。

模型不确定性的风险中性等价定价

The Risk-Neutral Equivalent Pricing of Model-Uncertainty

本文提出在模型不确定性下，通过强调约束而非偏好，将资产定价分解为模型与非模型风险，得到独特定价公式，并利用动量与低风险异象分离事前风险溢价与偏差。

金融相对论：资产定价的信息几何解释

Financial Relativity: An Information-Geometric Interpretation of Asset Pricing

本文提出金融相对论，通过信息几何重新解释资产定价，将风险中性测度视为后验概率几何，揭示价格波动、事件驱动行为和风险溢价的统一解释。

无无风险资产情形下由 Lévy 过程驱动的期权定价

Lévy-Driven Option Pricing without a Riskless Asset

本文扩展 LR 期权定价框架，在两种风险资产中引入共同 Lévy 跳跃，以内生影子利率替代无风险利率，并通过 LR-PIDE 与 FFT/COS 定价，显著改进 S&P 500 期权拟合。

Indifference pricing of pure endowments via BSDEs under partial information

In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset a…

Optimal Investment, Demand and Arbitrage under Price Impact

This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is gen…

Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition

This paper investigates the large-time asymptotic behavior of the sensitivities of cash flows. In quantitative finance, the price of a cash flow is expressed in terms of a pricing operator of a Markov diffusion process. We study the extent to which the pricing operator is affected by small changes of the underlying Markov diffusion. The main idea is a partial differential equation (PDE) representation of the pricing operator by incorporating the Hansen--Scheinkman decomposition method. The sensitivities of the cash flows and their large-time convergence rates can be represented via simple expr…