Dynamic indifference pricing via the G-expectation

Utility indifference pricing and hedging for structured contracts in energy markets

In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer's utility indifference price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates fo…

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…

Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein (2002). The price is determined by two optimal stochastic control problems (mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations. By means of backward stochastic differential equation and …

Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduce the notion of a weak and a strong certainty equivalent. We will show that our definitions contain as special cases some definitions found in the literature so far on complete or special incomplete preferences. We prove monotonicity and convexity properties of utility buy and se…

The pricing of contingent claims and optimal positions in asymptotically complete markets

We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated Gärtner-Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed m…

Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs

We consider indifference pricing of contingent claims consisting of payment flows in a discrete time model with proportional transaction costs and under exponential disutility. This setting covers utility maximisation as a special case. A dual representation is obtained for the associated disutility minimisation problem, together with a dynamic procedure for solving it. This leads to efficient and convergent numerical procedures for indifference pricing, optimal trading strategies and shadow prices that apply to a wide range of payoffs, a large range of time steps and all magnitudes of transac…

模糊环境下投资-消费框架中的数据资产定价模型

Pricing Model for Data Assets in Investment-Consumption Framework with Ambiguity

本文从买方视角提出一种基于信息价值的数据资产定价模型，利用模糊市场下稳健投资-消费问题中的无差异定价原理，推导出价格表达式并给出数值示例。

关于随机偏微分方程及其通过条件Feynman-Kac公式在衍生品定价中的应用

On Stochastic Partial Differential Equations and their applications to Derivative Pricing through a conditional Feynman-Kac formula

本文通过条件Feynman-Kac公式将金融衍生品价格表示为迭代条件期望，证明内层条件期望满足一个随机偏微分方程，并引入新的数值方法。

The relations of Choquet Integral and G-Expectation

In incomplete financial markets, there exists a set of equivalent martingale measures (or risk-neutral probabilities) in an arbitrage-free pricing of the contingent claims. Minimax expectation is closely related to the $g$-expectation which is the solution of a certain stochastic differential equation. We show that Choquet expectation and minimax expectation are equal in pricing European type options, whose payoff is a monotone function of the terminal stock price $S_T$.

在G期望框架下的期权定价模型

Option pricing model under the G-expectation framework

本文在G期望框架下开发了统一的风险中性估值方法，提出非线性Black-Scholes方程，并通过对数变换和有限差分方案提升计算效率与稳定性。

基于G-BSDE的稳健定价核长期分解方法

A G-BSDE approach to the long-term decomposition of robust pricing kernels

本文在G-期望框架下提出基于三类二次G-BSDE的定价核长期分解方法，将定价核唯一分解为指数贴现、暂时性、对称G-鞅和波动率不确定性递减四个分量，并用二阶PDE表示。

Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bonds

In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis. The results are compared with the numerical solution of the corresponding partial differential equation.

Expectation and Price in Incomplete Markets

Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price measure from the economic measure, subject to mark-to-market constraints, following arguments based on the optimisation of portfolio risk. The approach accounts for market and funding convexities and incorporates available price information, interpolating between methodologies based on expectation and replication.