A BSDE-based approach for the optimal reinsurance problem under partial information

We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton-Jacobi-Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process.Comment: 30 pages, 3 figure

GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization

In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general c\`adl\`ag martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of F\"ollmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994).Comment: 22 page

Detailed analysis of eta production in proton-proton collisions

The check whether the presently available multiresonance coupled channel analyses can explain the more complex processes is made. The process chosen is a well measured proces of eta production in proton proton collisions.Comment: 4 pages, talk given at N*2001 Workshop on the Physics of Excited Nucleons, 2001 Main

Optimal excess-of-loss reinsurance for stochastic factor risk models

We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate $r$. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed

On a Linearized Problem Arising in the Navier-Stokes Flow of a Free Liquid Jet

In this work, we analyze a Stokes problem arising in the study of the Navier-Stokes flow of a liquid jet. The analysis is accomplished by showing that the relevant Stokes operator accounting for a free surface gives rise to a sectorial operator which generates an analytic semigroup of contractions. Estimates on solutions are established using Fourier methods. The result presented is the key ingredient in a local existence and uniqueness proof for solutions of the full nonlinear problem

The Zakai equation of nonlinear filtering for jump-diffusion observation: existence and uniqueness

This paper is concerned with the nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any time t, the sigma-algebra generated by the observation process Y provides all the available information about the signal X. The central goal of stochastic filtering is to characterize the filter which is the conditional distribution of X, given the observed data. It has been proved in Ceci-Colaneri (2012) that the filter is the unique probability measure-valued process satisfying a nonlinear stochastic equation, the so-called Kushner-Stratonovich equation (KS-equation). In this paper the aim is to describe the filter in terms of the unnormalized filter, which is solution to a linear stochastic differential equation, called the Zakai equation. We prove equivalence between strong uniqueness for the solution to the Kushner Stratonovich equation and strong uniqueness for the solution to the Zakai one and, as a consequence, we deduce pathwise uniqueness for the solutions to the Zakai equation by applying the Filtered Martingale Problem approach (Kurtz-Ocone (1988), Kurtz-Nappo (2011), Ceci-Colaneri (2012)). To conclude, we discuss some particular cases.Comment: 29 page

Nucleon resonances and processes involving strange particles

An existing single resonance model with S11, P11 and P13 Breit-Wiegner resonances in the s-channel has been re-applied to the old pi N --> K Lambda data. It has been shown that the standard set of resonant parameters fails to reproduce the shape of the differential cross section. The resonance parameter determination has been repeated retaining the most recent knowledge about the nucleon resonances. The extracted set of parameters has confirmed the need for the strong contribution of a P11(1710) resonance. The need for any significant contribution of the P13 resonance has been eliminated. Assuming that the Baker. et al data set\cite{Bak78} is a most reliable one, the P11 resonance can not but be quite narrow. It emerges as a good candidate for the non-strange counter partner of the established pentaquark anti-decuplet.Comment: 5 pages, 2 figures, contribution to the NSTAR 2004 conference in Grenobl