Dynamic State Tameness

State Tameness: A New Approach for Credit Constrains

We propose a new definition for tameness within the model of security prices as Itô processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contingent claims of the American type. The valuation of European contingent claims and American contingent claims that we obtain does not require the full range of the volatility matrix. The technique used to prove the theorem on valuation of American contingent claims does not depend…

A Monte Carlo method for exponential hedging of contingent claims

Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming, which in practise can be difficult to implement. This article presents a Monte Carlo approach to optimal portfolio problems for which the dynamic programming is based on the exponential utility function U(x)=-exp(-x). The algorithm, inspired by the Longstaff-Schwartz approach to pricing American options by Monte Carlo simulation, involves learning the optimal p…

生命或有风险的动态资产定价理论

Dynamic Asset Pricing Theory for Life Contingent Risks

本文在无套利完备市场框架下，利用资产定价基本定理推导生命或有资产（人寿保险与年金）的估值公式，并阐明动态经济中静态投资组合的适用条件。

美式衍生品的风险无关定价

Risk-indifference Pricing of American-style Contingent Claims

本文研究了美式衍生品的定价，采用动态凸风险度量进行无关定价，定义了买卖方在连续时间下的风险无关价格，并展示了其与无套利原则的一致性，通过随机波动模型证明了其在深度学习数值方法中的应用基础。

Pricing, Hedging and Optimally Designing Derivatives Via Minimization of Risk Measures

The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in the literature to provide a satisfactory answer to this problem, for a particular choice criterion. In this paper, in order to price and hedge a non-tradable contingent claim, we first start with a (standard) utility maximization problem and end up with an equivalent risk measure minimization. This hedging problem can be seen as a particular case of a more ge…

A pricing formula for delayed claims: Appreciating the past to value the future

We consider the valuation of contingent claims with delayed dynamics in a Black&Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity. The formula we derive has successfully been used to explicitly solve the infinite dimensional stochastic control problems addressed in d…