The optimal reinsurance problem is a classic topic in Actuarial Mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the...

Value-at-Risk (VaR) models often are used to estimate the equity investment that is required to limit the default rate on funding debt. Typical VaR "buffer stock" capital calculations produce biased estimates. To ensure accuracy, VaR must be modified by: (1) measuring loss relative to initial...

The classes of reward-risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for...

Risk, in a financial sense, is defined as variance about some forecasted value. Any time a business appraiser forecasts future cash flows of any sort, these future value estimates are actually means of all likely cash flows in that particular year. The same holds true with discount rate...

This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating...

General risk functions are becoming very important in finance and insurance. Many risk functions are interpreted as initial capital requirements that a manager must add and invest in a risk-free security in order to protect his clients wealth. Nevertheless, until now it has not been proved that...

We study a new risk measure inspired from risk theory with a heat wave risk analysis motivation. We show that this risk measure and its sensitivities can be computed in practice for relevant temperature stochastic processes. This is in particular useful for measuring the potential impact of...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of...