Supermodular ordering and stochastic annuities.

In this paper, we consider several types of stochastic annuities, for which an explicit expression of the distribution function is not available. We will construct a random variable with the same mean and which is larger in stop-loss order, for which the distribution function can be easily obtained.annuities;

Self exciting threshold interest rates models.

In this paper, we study a new class of tractable diffusions suitable for model's primitives of interest rates. We consider scalar diffusions with scale s'(x) and speed m(x) densities discontinuous at the level x*. We call that family of processes Self Exciting Threshold (SET) diffusions. Following Gorovoi and Linetsky (2004), we obtain semianalytical expressions for the transition density of SET (killed) diffusions. We propose several applications to interest rates modeling. We show that SET short rate processes do not generate arbitrage possibilities and we adapt the HJM procedure to forward rates with discontinuous scale density. We also extend the CEV and the shiftedlognormal Libor market models. Finally, the models are calibrated to the U.S. market. SET diffusions can also be used to model stock price, stochastic volatility, credit spread, etc.Eigenfunction expansions; Interest rates; Market models; SETAR; Skew Brownian motion; State-price density;

On the characterization of Wang's class of premium principles.

A premium principle is an economic decision rule used by the insurer in order to determine the amount of the net premium for each risk in his portfolio. In this paper we investigate the problem of determining the premium principle to be used. First, we discuss some desirable properties of a premium principle. We prove that the only premium principles that possess these properties belong to a class of premium principles introduced by Wang (1996). Similar results ccan be found in Wang, Young & Panjer (1997)..Principles;

On the dependency of risks in the individual life model.

The paper considers several types of dependencies between the different risks of a life insurance portfolio. Each policy is assumed to having a positive face amount (or an amount at risk) during a certain reference period. The amount is due if the policy holder dies during the reference period.First, we will look for the type of dependency between the individuals that gives rise to the riskiest aggregate claims in the sense that it leads to the largest stop-loss premiums. Further, this result is used to derive results for weaker forms of dependency, where the only non-independent risks of the portfolio are the risks of couples (wife and husband).Model; Risk; Dependency; Life insurance; Insurance; Portfolio; Stop-loss premium;

Dependency of risks and stop-loss order.

The correlation order, which is defined as a partial order between bivariate distributions with equal marginals, is shown to be a helpfull tool for deriving results concerning the riskiness of portfolios with pairwise dependencies. Given the distribution functions of the individual risks, it is investigated how changing the dependency assumption influences the stop-loss premiums of such portfolios.Risk; Correlation order; Distribution; Portfolio; Dependency; Functions; Stop-loss premium;

Actuarial applications of financial models.

In the present contribution we indicate the type of situations seen from an insurance point of view, in which financial models serve as a basis for providing solutions to practical problems . In addition, some of the essential differences in the basic assumptions underlying financial models and actuarial applications are given.Actuarial; Applications; Model; Models;

Pricing exotic options under local volatility.

Optimal; Optimal portfolio selection; Portfolio; Selection; Cash flow; Capital at risk; Risk; Pricing; Options;

Solution of the Fokker-Planck equation with boundary conditions by Feynman-Kac integration.

In this paper, we apply the results about d and d-function perturbations in order to formulate within the Feynman-Kac integration the solution of the forward Fokker-Planck equation subject to Dirichlet or Neumann boundary conditions. We introduce the concept of convex order to derive upper and lower bounds for path integrals with d and d- functions in the integrand. We suggest the use of bounds as an approximation for the solution.Feynman-Kac integration; Functions; Integration; Path integral; Perturbations theory; SDE;