On States of Total Weighted Occupation Times of a Class of Infinitely Divisible Superprocesses on a Bounded Domain

In this paper, general conditions of state classification for the total weighted occupation times of a class of infinitely divisible superprocesses on a bounded domain D in ℝ ^d are given. As an application, some sufficient and necessary conditions are found for the total weighted occupation times of some special superprocesses on D to be absolutely continuous or singular with respect to the Lebesgue measure on D. The research of Yan-Xia Ren is supported by NNSF of China (Grant No. 10471003) and Foundation for Authors Awarded Excellent Ph.D. Dissertation.     

Asset and liability modelling for participating policies with guarantees

We study the problem of asset and liability management of participating insurance policies with guarantees. We develop a scenario optimization model for integrative asset and liability management, analyze the tradeoffs in structuring such policies, and study alternative choices in funding them. The nonlinearly constrained optimization model can be linearized through closed form solutions of the dynamic equations. Thus large-scale problems are solved with standard methods. We report on an empirical analysis of policies offered by Italian insurers. The optimized model results are in general agreement with current industry practices. However, some inefficiencies are identified and potential improvements are highlighted.     

Theory of optimal consumption and portfolio selection under a Capital-at-Risk (CaR) and a Value-at-Risk (VaR) constraint

The solution to the optimal portfolio selection and consumptionrule subject to Capital-at-Risk and Value-at-Risk constraintsis derived via the use of stochastic dynamic programming.     

Asymmetric impacts of global risk appetite on the risk premium for an emerging market

This paper analyzes the impact of global risk appetite on the risk premium utilizing high-frequency data. Taking the Turkish economy as our laboratory, we find that the risk premium volatility responds only to a worsening in the risk appetite for the Turkish economy, which is a result that we do not observe for the other emerging markets. Then, we investigate the role of current account dynamics on this asymmetric effect, by focusing also on an economy with similar current account performance. The empirical results find supporting evidence for the role of current account dynamics on the estimated asymmetry.     

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.     

Absolute continuity of Wasserstein geodesics in the Heisenberg group

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot, Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2) (2004) 261-301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below.     

Dual characterization of properties of risk measures on Orlicz hearts

We extend earlier representation results for monetary risk measures on Orlicz hearts. Then we give general conditions for such risk measures to be Gateaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoretical results are used to analyze various specific examples of risk measures. We thank Andreas Hamel and Michael Kupper for fruitful discussions and helpful comments. P. Cheridito has been supported by NSF Grant DMS-0642361, a Rheinstein Award and a Peek Fellowship. T. Li has been supported by a Marshall Scholarship and a Merage Fellowship.     

The Absolute of a Topological Space and its Application to Abelian l-groups

We give a axiomatic treatment of the absolute in the category of all topological spaces and characterize it as a cover with respect to the full subcategory of extremally disconnected spaces. As an application, we obtain the strongly projectable hull of an abelian l-group as a unique lifting of the absolute of its spectrum. Dedicated to B. V. M.