Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints

This paper studies the risk management in a defined contribution (DC)pension plan. The financial market consists of cash, bond and stock. The interest rate in our model is assumed to follow an Ornstein–Uhlenbeck process while the contribution rate follows a geometric Brownian Motion. Thus, the pension manager has to hedge the risks of interest rate, stock and contribution rate. Different from most works in DC pension plan, the pension manger has to obtain the optimal allocations under loss aversion and Value-at-Risk(VaR) constraints. The loss aversion pension manager is sensitive to losses while the VaR pension manager has to ensure the quality of wealth at retirement. Since these problems are not standard concave optimization problems, martingale method is applied to derive the optimal investment strategies. Explicit solutions are obtained under these two optimization criterions. Moreover, sensitivity analysis is presented in the end to show the economic behaviors under these two criterions.     

Small Sample Asymptotics for Credit Risk Portfolios

This article considers small sample asymptotics for the distribution of the total loss S_n of a credit risk portfolio. For portfolios with a few exceptionally high potential loss values, the distribution of S_n turns out to be bimodal. Direct approximation by Esscher tilting does not capture this feature. An improved recursive algorithm is proposed. The new approach leads to a more accurate small sample approximation that models bimodality in the presence of outliers. The results are illustrated by a simulated example as well as an example of an observed credit risk portfolio.     

On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flowSur une fermeture des équations de conservation de la masse et l'analyse de la stabilité dans la théorie mathématique de la circulation véhiculaire

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow. To cite this article: V. Coscia, C. R. Mecanique 332 (2004).     

Fluctuation analysis for the loss from default

We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Numerical results illustrate the accuracy and computational efficiency of the approximation.     

Robustness of optimal portfolios under risk and stochastic dominance constraints

Solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation, estimation and incomplete information. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. We shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity-based global contamination bounds. Results obtained in our paper [Dupa?ová, J., & Kopa, M. (2012). Robustness in stochastic programs with risk constraints. Annals of Operations Research, 200, 55–74.] were derived for the risk and second order stochastic dominance constraints under suitable smoothness and/or convexity assumptions that are fulfilled, e.g. for the Markowitz mean–variance model. In this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints. Local bounds for problems of a special structure are obtained. Under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test.     

Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market

We propose a way of using DEA cross-efficiency evaluation in portfolio selection. While cross efficiency is an approach developed for peer evaluation, we improve its use in portfolio selection. In addition to (average) cross-efficiency scores, we suggest to examine the variations of cross-efficiencies, and to incorporate two statistics of cross-efficiencies into the mean-variance formulation of portfolio selection. Two benefits are attained by our proposed approach. One is selection of portfolios well-diversified in terms of their performance on multiple evaluation criteria, and the other is alleviation of the so-called “ganging together” phenomenon of DEA cross-efficiency evaluation in portfolio selection. We apply the proposed approach to stock portfolio selection in the Korean stock market, and demonstrate that the proposed approach can be a promising tool for stock portfolio selection by showing that the selected portfolio yields higher risk-adjusted returns than other benchmark portfolios for a 9-year sample period from 2002 to 2011.     

Investment under duality risk measure

One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for so-called gambles satisfies the duality and positive homogeneity axioms. We call it a duality index. This paper extends the definition of duality index to all outcomes including all gambles, and considers a portfolio selection problem in a complete market, in which the agent’s target is to minimize the index of the utility of the relative investment outcome. By linking this problem to a series of Merton’s optimum consumption-like problems, the optimal solution is explicitly derived. It is shown that if the prior benchmark level is too high (which can be verified), then the investment risk will be beyond any agent’s risk tolerance. If the benchmark level is reasonable, then the optimal solution will be the same as that of one of the Merton’s series problems, but with a particular value of absolute risk aversion, which is given by an explicit algebraic equation as a part of the optimal solution. According to our result, it is riskier to achieve the same surplus profit in a stable market than in a less-stable market, which is consistent with the common financial intuition.     

Students’ coordination of lower and higher dimensional units in the context of constructing and evaluating sums of consecutive whole numbers

This paper examines how three eighth grade students coordinated lower and higher dimensional units (e.g., composite units and pairs) in the context of constructing a formula for evaluating sums of consecutive whole numbers while solving combinatorics problems (e.g., 1 + 2 + ⋯ + 15 = (16 × 15)/2). The data is drawn from the beginning of an 8-month teaching experiment. The findings from the study include: (1) a framework for understanding how students coordinate lower and higher dimensional units; (2) identification of key learning that occurred as students made the transition between solving two kinds of combinatorics problems; and (3) identification of the links between the way students’ coordinated lower and higher dimensional units and their evaluation of sums of consecutive whole numbers. Implications for research and teaching are considered.     

Optimal portfolio choice for an insurer with loss aversion

The problem of optimal investment for an insurance company attracts more attention in recent years. In general, the investment decision maker of the insurance company is assumed to be rational and risk averse. This is inconsistent with non fully rational decision-making way in the real world. In this paper we investigate an optimal portfolio selection problem for the insurer. The investment decision maker is assumed to be loss averse. The surplus process of the insurer is modeled by a Lévy process. The insurer aims to maximize the expected utility when terminal wealth exceeds his aspiration level. With the help of martingale method, we translate the dynamic maximization problem into an equivalent static optimization problem. By solving the static optimization problem, we derive explicit expressions of the optimal portfolio and the optimal wealth process.     

Optimal payoff under the generalized dual theory of choice

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari’s dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The optimal portfolio yields an in-the-money payoff when the market is good and zero payoff otherwise. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff.