We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk...

We analyze a problem of maximization of expected terminal wealth and consumption under constraints in a general framework including financial models with constrained portfolios, labor income and large investor models. By using general optional decomposition under constraints in a multiplicative...

We analyze a problem of maximization of expected terminal wealth and consumption in markets with some ``imperfection'', such as constraints on the permitted portfolios, labor income, or/and nonlinearity of portfolio dynamics. By using general optional decomposition under constraints in...

We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some ``imperfection'', such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition...

We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We...

Value-at-Risk (VaR) determines the probability of a portfolio of assets losing a certain amount in a given time period due to adverse market conditions with a particular level of confidence. Value-at-Risk has received considerable attention from financial economists and financial practitioners...

This article is devoted to the study cashflow maps used in the computation of value-at-risk (VaR). Properties and characteristics of the approaches found in the literature are presented and two new approaches are introduced. The goal of this paper is to study the quality of these maps. This is...

In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (VaR), are studied from the perspective of the theory of coherent imprecise previsions. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be...

This note describes the problem arising from using a currency basket in the computation of value-at-risk. This applies mainly when the basket is used as base currency. A solution based on the modification of the historical time series is proposed. The solution is easy to implement and doesn't...

We measure the loss potential of Hedge Funds by combining three market risk measures: VaR, Draw-Down and Time Under-The-Water. Calculations are carried out considering three different frameworks regarding Hedge Fund returns: i) Normality and time-independence, ii) Non-normality and time-...