In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random...

In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in finance when we want to find an investment strategy and an investment portfolio which should replicate a liability or...

In this paper we investigate an asset-liability management problem for a stream of liabilities written on liquid traded assets and non-traded sources of risk. We assume that the financial market consists of a risk-free asset and a risky asset which follows a geometric Lévy process. The...

We investigate solutions of backward stochastic differential equations (BSDEs) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Lévy process. In these new types of equations, the generator can depend on the past values...

In this paper we deal with backward stochastic differential equations and give examples of their applications to insurance and finance. There are two major fields of applications. The first area concerns pricing and risk measures, the second deals with optimal control problems and optimization....

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant...

We investigate the problem of pricing and hedging variable annuity contracts for which the fee deducted from the policyholder’s account depends on the account value. It is believed that state-dependent fees are beneficial to policyholders and insurers since they reduce policyholders’...

In this paper we deal with market-consistent valuation and hedging of insurance cash flows. We start with recalling traditional actuarial and financial pricing principles and we show how to integrate them into one arbitrage-free principle which leads to market-consistent valuation of the cash...

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant...

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π10 a new vertex with one edge attached to it is added to the network and the edge is...