Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm

Abstract

The minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging. There are two major reasons. Firstly, heavy tails and the lack of symmetry in the returns of many assets provokes that the classical opti mization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several general risk or dispersion measures. The representation the orems of risk functions are applied to transform the general risk minimization problem in a minimax problem, and later in a linear pro gramming problem between infinite dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex like algorithm is developed. The algorithm solves the dual problem and provides both optimal portfolios and their sensitivities.The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are spe cially analyzed. A final real data numerical example illustrates the practical performance of the proposed methodology.

Good Deals and compatible modification of risk and pricing rule: a regulatory treatment

“…This problem has been studied in Balbás et al [3,2,4]. The dual of problem (3.4) is found in Balbás et al [3] as…”

Human Resources Risk Element Transmission Model of Construction Project Based on System Dynamic

“…The situation corresponding to working overtime has been studied in the literature [13], therefore, only the phenomenon of delay resulting from the new devotion of human resource will be considered in this paper.…”

“…This approach avoided human influence factor in expert assessment method, and had a good effect on risk decision making. Alejandro Balbás transformed the risk function into an infinite-dimensional Banach space of linear programming, and gave the general simplex algorithm [13], which made good application in investment portfolio and the optimal hedge. Other methods such as artificial neural networks [14], genetic algorithms [15], Monte Carlo simulation [16], risk assessment [17] and multi-agent [18] were used to solve the project risks problems.…”

Hedging and Pricing in Imperfect Markets Under Non-Convexity

“…This non-parametric or robust hedging approach 1 is fairly general and can be used for various purposes such as hedging contingent claims and economic risk variables. While it encompasses the methods developed in Jaschke and Küch-ler (2001), Staum (2004), Xu (2006), Assa and Balbás (2011), Balbás, Balbás, and Heras (2009), Balbás, Balbás, and Garrido (2010), Mayoral (2009), andArai andFukasawa (2014) for sub-additive risk measures and pricing rules, the main novelty of this paper lies in incorporating possibly non-convex risk measures which are extensively used in practice. For example, the celebrated Value at Risk and risk measures related to Choquet expected utility (Bassett, Koenker, and Kordas (2004)) are, in general, non-convex.…”

“…The robust pricing and hedging strategies of Cox and Ob÷ ój (2011b) and Cox and Ob÷ ój (2011a) serve as an example of this approach. A di¤erent line of research in model-free hedging is based directly on the concepts of hedging and minimization of risk (see Xu (2006), Assa and Balbás (2011), Balbás, Balbás, and Heras (2009), Balbás, Balbás, and Garrido (2010), and Balbás, Balbás, and Mayoral (2009)). In this setting, the investor or portfolio manager minimizes the risk of a global position given the budget constraint on a set of manipulatable positions (a set of accessible portfolios, for instance).…”