arXiv 1102.39282011-02math.OCq-fin.RM

Integral representations of risk functions for basket derivatives

Michał Barski

备注：: 25 pages
发表信息：: Applicationes Mathematicae, 2012, 39, 489-514

英文摘要：

The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,π})^{+})]\oversetπ{\longrightarrow}\min$ in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for $l(x)=x$ and $l(x)=x^p$, with $p>1$ for digital, quantos, outperformance and spread options are derived.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

保险衍生产品的最优交叉套期保值

Optimal cross hedging for insurance derivatives

我们认为保险衍生产品取决于外部物理风险过程，例如在低维气候模型中的温度。我们假设这一过程与可交易金融资产相关。我们从终端财富中推导出指数效用的最优策略，确定衍生品的无差别价格，并从多元化压力的角度解释它们。此外，我们检查标准的容许准则的最优投资策略。最后，我们比较了静态风险与保险衍生品的风险降低，由于动态投资到相关资产。我们表明，动态套期保值降低了风险规避熵风险措施的相关性的一个因素。

2007-05-25math.OCmath.PRq-fin.PR

Weak Convergence of Equity Derivatives Pricing with Default Risk

This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we deduce the Arrow--Debreu state prices and the explicit pricing result in discrete time after embedding default risk in the pricing model. We prove that the discrete--time defaultable equity derivatives pricing has convergence stability, and it converges weakly to the continuous--time pricing results.

2015-04-10math.OCmath.PR

Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments

This paper studies the equal risk pricing (ERP) framework for the valuation of European financial derivatives. This option pricing approach is consistent with global trading strategies by setting the premium as the value such that the residual hedging risk of the long and short positions in the option are equal under optimal hedging. The ERP setup of Marzban et al. (2020) is considered where residual hedging risk is quantified with convex risk measures. The main objective of this paper is to assess through extensive numerical experiments the impact of including options as hedging instruments w…

2021-02-25math.OCq-fin.CPq-fin.RM

基于或有信用风险控制的最优盯市时机研究

Study on optimal timing of mark-to-market for contingent credit risk control

场外交易衍生工具大大提高了国际金融体系的效力和效率，但也带来了重大的交易对手信用风险。抵押是衍生品交易中最重要和最广泛使用的信用风险缓解技术之一。然而，有关决定往往是临时作出的，没有参照分析框架。学术界对抵押品风险控制的定量研究较少。由于按市价计值的难度和成本，按市价计值的时机选择问题对于减少非流动性和长期衍生品合约的信用风险变得重要。本研究的目标是提出一个框架，通过优化按市价计值的时间安排，尽量减少有抵押衍生工具交易的潜在信贷风险。

2005-06-04math.OCmath.PRq-fin.RM

核之间的积分输运距离与马尔可夫系统中的近似动态风险评估

An Integrated Transportation Distance Between Kernels and Approximate Dynamic Risk Evaluation in Markov Systems

该研究提出核间积分输运距离并证明其为度量，将其用于马尔可夫正倒向系统的递归近似与风险评估误差估计，还开发了基于粒子的数值方法，在美式篮子期权定价等问题中验证了有效性。

2023-11-11math.OC

Equal Risk Pricing and Hedging of Financial Derivatives with Convex Risk Measures

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we establish that the problem reduces to solving independently the writer and the buyer's hedging problem with zero initial capital. By further imposing that the risk measures decompose in a way that satisfies a Markovian property, we provide dynamic programming equations that can be used to solve the hedgin…

2020-09-16math.OCq-fin.PR

更多相关论文收起更多论文

A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing

We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with strong ave…

2018-01-03math.OCq-fin.MF

Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexity

University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）

Direct policy search serves as one of the workhorses in modern reinforcement learning (RL), and its applications in continuous control tasks have recently attracted increasing attention. In this work, we investigate the convergence theory of policy gradient (PG) methods for learning the linear risk-sensitive and robust controller. In particular, we develop PG methods that can be implemented in a derivative-free fashion by sampling system trajectories, and establish both global convergence and sample complexity results in the solutions of two fundamental settings in risk-sensitive and robust co…

2021-12-30cs.AIcs.LGcs.SY

Risk aware minimum principle for optimal control of stochastic differential equations

We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions in which the risk neutral expectation is replaced by a risk function, a nonlinear functional of random variables that account for the controller's risk preferences. We state and prove a risk aware minimum principle that is a parsimonious generalization of the well-known risk neutral, stochastic Pontryagin's minimum principle. As our main results we give necessary and also sufficient conditions for optimality of c…

2019-10-19math.OC

非线性分布鲁棒优化

Nonlinear Distributionally Robust Optimization

Delft University of Technology（代尔夫特理工大学）；Delft Center for Systems and Control（代尔夫特系统与控制中心）

本文针对目标函数在分布上非线性的分布鲁棒优化问题，提出基于Gateaux导数的光滑性概念和Frank-Wolfe算法，实现独立于范数的收敛，并应用于投资组合选择中的熵风险与方差风险，验证了理论结果。

2024-11-05cs.LGmath.OCstat.ML

具有形状导数信息的神经算子及其在风险规避形状优化中的应用

Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization

Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA（奥登计算工程与科学研究所，德克萨斯大学奥斯汀分校，奥斯汀，德克萨斯，美国）；School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia（数学科学学院，昆士兰科技大学，布里斯班，澳大利亚）；Centre for Data Science, Queensland University of Technology, Brisbane, Australia（数据科学中心，昆士兰科技大学，布里斯班，澳大利亚）；Department of Mathematics, The Ohio State University, Columbus, Ohio, USA（数学系，俄亥俄州立大学，哥伦布，俄亥俄，美国）；Department of Engineering Science and Biomedical Engineering, University of Auckland, Auckland, New Zealand（工程科学与生物医学工程系，奥克兰大学，奥克兰，新西兰）；Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, USA（沃克机械工程系，德克萨斯大学奥斯汀分校，奥斯汀，德克萨斯，美国）

Shape-DINO通过导数信息驱动的神经算子框架，提升PDE约束下形状优化的效率和准确性，实现大规模不确定性下的形状优化。

2026-03-03cs.LGcs.NAmath.NA