Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

Utility theory and insurance -- The individual risk model -- Collective risk models -- Ruin theory -- Premium principles -- Bonus-malus systems -- Credibility theory -- Generalized linear models -- IBNR techniques -- Ordering of risks.

In this paper we examine and summarize properties of several well-known risk measuresthat can be used in the framework of setting solvency capital requirements for a risky business.Special attention is given to the class of (concave) distortion risk measures. We investigatethe relationship...

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process, and a shifted inverse Gaussian process to describe the logarithm of the stock...

We investigate multiperiod portfolio selection problems in a Black and Scholes type market where a basket of 1 riskfree and "m" risky securities are traded continuously. We look for the optimal allocation of wealth within the class of "constant mix" portfolios. First, we consider the portfolio...