论文标题
最小化用于马尔可夫决策过程的光谱风险措施
Minimizing Spectral Risk Measures Applied to Markov Decision Processes
论文作者
论文摘要
我们研究了马尔可夫决策过程（MDP）在有限或无限计划范围内产生的总折扣成本的光谱风险度量的最小化。假定MDP具有Borel状态和动作空间，并且成本函数可能在上面无限。优化问题使用频谱风险度量的ige最小表示分为两个最小化问题。我们表明，内部最小化问题可以在扩展的状态空间上作为普通MDP解决，并提供足够的条件，在这些条件下存在最佳政策。关于无限的尺寸外部最小化问题，我们证明了解决方案的存在，并得出了其数值近似的算法。我们的结果包括Bäuerle和Ott（2011）中的发现，即预计风险措施不足。作为应用程序，我们提出了经典静态最佳再保险问题的动态扩展，其中保险公司将其资本成本降至最低。
We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in Bäuerle and Ott (2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.
