We consider a dynamic reinsurance market, where the traded risk process is driven by a jump-diffusion and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the...

Although financial risk measurement is a largely investigated research area, its relationship with imprecise probabilities has been mostly overlooked. However, risk measures can be viewed as instances of upper (or lower) previsions, thus letting us apply the theory of imprecise previsions to them. After a presentation of some well known risk measures, including Value-at-Risk or VaR, coherent an...

In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of the complete mixability, we provide a new lower bound for any...

In a continuous time, arbitrage free, non-complete market with a zero bond, we nd the intertemporal price for risk to equal the standard deviation of the discounted variance optimal martingale measure divided by the zero bond price. We show the Hedging Num eraire to equal the Market Portfolio and nd the mean-variance eÆcient portfolios.

The results of a complete one-loop calculation for the fermionic decay width Γ(h 0 , H 0 , A 0 → f ¯ f) of the neutral MSSM Higgs bosons are presented and the dominant light Higgs decay channel h 0 → b ¯ b is discussed in detail. The enhancement of Γ(h 0 → b ¯ b) compared to the standard Higgs decay is shown for pseudoscalar masses M A ≤ 300 GeV, where the one-loop contributions in the MSSM and...

In arbitrage-free but incomplete markets, the equivalent martingale measure Q for pricing traded assets is not uniquely determined. A possible approach when it comes to choosing a particular pricing measure is to consider the one that is ‘closest’to the physical probability measure P, where closeness is measured in terms of relative entropy. In this paper, we determine the minimal entropy marti...

This paper studies by means of reciprocal fuzzy binary relations the aggregation of preferences when individuals show their preferences gradually. We have characterized neutral aggregation rules through functions from powers of the unit interval in the unit interval. Furthermore, we have determined the neutral aggregation rules that are decomposable and anonymous. In this class of rules, the co...

We construct a continuous bounded stochastic process (St)t2[0;1] which admits an equivalent martingale measure but such that the minimal martingale measure in the sense of Follmer and Schweizer does not exist. This example also answers (negatively) a problem posed by I. Karatzas, J. P. Lehozcky and S. E. Shreve as well as a problem posed C. Stricker.

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. Formally, we apply a generalized version of Perron-Frobenius theory to construct this probability measure. We discuss methods for recovering this distribution from financial market data; we apply this distribution to characterize th...

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generaliz...