Summary We study reward over penalty for risk ratios E [ u ( V )]/ E [ρ( V )], V ∈ V , where V ⊆ L 1 ( P ) describes a linear space of attainable returns in an arbitrage-free market, u is concave and ρ ≥ 0 is convex. It turns out that maximizing such reward over penalty ratios is...

SUMMARY For a monetary utility functional U and a coherent risk measure ρ, both with compact scenario sets in L q , we optimize the ratio α( V ): = U ( V )/ρ( V ) over an (arbitrage-free) linear sub-space V ⊆ L p , 1 ≤ p ≤ ∞, of attainable returns in an incomplete market model such...

SUMMARY The purpose of our paper is to link some results on the Choquet integrals with the theory of coherent risk measures. Using this link we establish some properties of dilatation monotone and comonotonic coherent measures of risk. In particular it is shown that on an atomless probability...

Summary Using a backward stochastic differential equation (BSDE) approach in a Brownian motion setting, we determine in an incomplete market an initial price Y 0 for a non-attainable claim ξ ∈ L p , 1 p ∞, that takes the hedging risk into account. Y 0 is chosen to be the best price such...

The empirical performance of macroeconomic exchange rate models is more than disappointing. This dismal result is also reflected in the forecasting capabilities of professional analysts: all in all, analysts are not in a position to beat naïve random walk forecasts. The root for this deficient...

We propose a new valuation principle for possibly non-traded assets based on an implicit definition of a benchmark. The valuation principle allows taking (default and shortfall) risk constraints explicitly into account. The resulting risk-adjusted value functional is monotonic, positively...

We present a decision theory appropriate for use in serious choices such as insurance. It extends standard decision theories like expected utility or cumulative prospect theory which are atemporal single stage theories. Instead it employs stages of knowledge ahead to track satisfactions and...

In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the convex conjugate of a generalized entropy penalty...