Булевозначный подход к анализу условного риска

By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, aconditional risk measure can be interpreted as a classical convex risk measure within asuitable set-theoretic model. As a consequence, many properties of a conditional risk measure can be interpreted as basic properties of convex risk measures. This amounts to a method to interpret a theorem ofdual representation of convex risk measures as a new theorem of dual representation of conditional risk measures. As an instance of application, we establish a general robust representation theorem for conditional risk measures and study different particular cases of it.

Optimal portfolio in the presence of transaction costs and convex risk measure

We analyze the optimal portfolio selection problem of maximizing the utility of an agent who invests in a stock and a money market account in the presence of transaction costs. The stock price follows a geometric process. The preference of the investor is assumed to follow the constant relative risk aversion (CRRA). We further investigate the risk minimizing portfolio through a zero-sum stochastic differential game (SDG). To solve this two-player SDG we use the Hamilton–Jacobi–Bellman–Isaacs (HJBI) for general zero-sum SDG in a jump setting.

GOOD DEAL BOUNDS WITH CONVEX CONSTRAINTS

We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai & Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk measure a good deal valuation; and study its properties. We also discuss superhedging cost and Fundamental Theorem of Asset Pricing for convex constrained markets.

A Convex-Risk-Measure Based Model and Genetic Algorithm for Portfolio Selection

A convex risk measure called weighted expected shortfall (briefly denoted as WES (Chen and Yang, 2011)) is adopted as the risk measure. This measure can reflect the reasonable risk in the stock markets. Then a portfolio optimization model based on this risk measure is set up. Furthermore, a genetic algorithm is proposed for this portfolio optimization model. At last, simulations are made on randomly chosen ten stocks for 60 days (during January 2, 2014 to April 2, 2014) from Wind database (CFD) in Shenzhen Stock Exchange, and the results indicate that the proposed model is reasonable and the proposed algorithm is effective.

Law-invariant risk measures: Extension properties and qualitative robustness

We characterize when a convex risk measure associated to a law-invariant acceptance set in

Asymptotics for Operational Risk Quantified with Expected Shortfall

In this paper we estimate operational risk by using the convex risk measure Expected Shortfall (ES) and provide an approximation as the confidence level converges to 100% in the univariate case. Then we extend this approach to the multivariate case, where we represent the dependence structure by using a Lévy copula as in Böcker and Klüppelberg (2006) and Böcker and Klüppelberg, C. (2008). We compare our results to the ones obtained in Böcker and Klüppelberg (2006) and (2008) for Operational VaR and discuss their practical relevance.