精算论坛讲座 第105期 - 程雪、彭江艳、Vali Asimit (7月7日)2017年06月27日 来源: 中国精算研究院
讲座题目一：Optimal Execution with Uncertain Order Fills and Dynamic Risk Measures
摘要： The problem of optimal execution is formulated as a stochastic control problem aiming at maximizing a generalized risk-adjusted profit and loss. The risk consists of a g-expectation and a cumulative dynamical risk measure. This formulation is on the one hand regarded as a natural generalization of utility maximization subject to a dynamical constraint on trading risks such as value at risk or expected shortfall. On the other hand, from economics viewpoint it is a generalization of maximizing the risk premia subject to constraints. We show that under certain technical conditions the stochastic control problem under consideration satisfies the dynamical programming principle. As an illustration, we work out examples with closed form and quasi closed form expressions in the Almgren-Chriss framework.
程雪老师于2009年在中国科学院应用数学所获得博士学位，专业为概率论与数理统计。主要研究兴趣为模型不确定情形资产定价问题，信用衍生品，及价格冲击模型相关问题等，曾在Quantitative Finance、Mathematics and Financial Economics、Science China Mathematics等杂志发表文章。现主持一项国家自然科学基金项目。
讲座题目二：Ruin Probability with Dependence Structures and Stochastic Investment Returns Weak convergence to stochastic integrals under primitive conditions in nonlinear econometric models
摘要：Consider a non-standard renewal risk model with dependence structures, where claim sizes follow a one-sided linear process with independent and identically distributed step sizes, the step sizes and inter-arrival times respectively form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. An insurance company is allowed to make risk-free and risky investments, where the price process of the investment portfolio follows an exponential Levy process. When the step-size distribution is dominatedly-varying-tailed, some asymptotic estimates for the finite-and infinite-time ruin probabilities are obtained. Further, we obtain that some uniform asymptotics for the finite-and infinite-time ruin probabilities.
Limit theory with stochastic integrals plays a major role in time series econometrics. In earlier contributions on weak convergence to stochastic integrals, the literature commonly uses martingale and semi-martingale structures. Liang et al. (2015) (see also Wang (2015), Chapter 4.5) currently extended weak convergence to stochastic integrals by allowing for a linear process in innovations. While these martingale and linear processes structures have wide relevance, they are not sufficiently general to cover many econometric applications that have endogeneity and nonlinearity. This paper provides new conditions for weak convergence to stochastic integrals. Our frameworks allow for long memory processes, causal processes, and near-epoch dependence in innovations, which have applications in a wide range of econometric areas, such as GARCH, TAR, bilinear, and other nonlinear models.
讲座题目三：Optimal reinsurance with multiple reinsurers
摘要：The optimal reinsurance contract has been a topic of great interest for many decades in the insurance literature. The primary insurer aims to share the risk with one or many other reinsurers for a premium. Finding the optimal contract has been a topic for a long time in insurance economics literature. Depending on how the problem is put, the solutions are different, but layer reinsurance appears to be optimal contract, which confirms the existing empirical evidence. In this talk, we will focus on finding the optimal contract from the perspective of primary reinsurer or from the perspective of all insurers. Interestingly, all solutions are optimal Pareto when all risk preferences have the translation invariance property. The robustness of the reinsurance contract is also discussed. Finally, we will show that introducing of some constraints, the optimal contract is no longer a layer reinsurance and instead, a proportional reinsurance contract appears to be the optimal one.
主讲人：Vali Asimit, Reader in Actuarial Science, Cass Business School, City University of London
Vali Asimit joined Cass in January 2011 as a Lecturer in Actuarial Science. Previously, he had been a Lecturer in Actuarial Science at the University of Manchester for two years. Vali had studied Economics at the Academy of Economic Studies, Bucharest, Romania. He has an MSc in Statistics from the University of Western Ontario, Canada. He pursued his doctoral research on "Dependence Modelling with Applications in Finance and Insurance" at the University of Western Ontario. As part of his academic work he has published and acted as referee for international statistical and actuarial journals. Vali received the 2010 Fortis Award for the best Insurance: Mathematics and Economics (IME) journal paper presented at the 14th International Congress of IME.
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