We consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market with stochastic interest rate. The fund...

In a financial market with one riskless asset and n risky assets following geometric Brownian motions, we solve the problem of a pension fund maximizing the expected CRRA utility of its terminal wealth. By considering a stochastic death time for a subscriber, we solve a unique problem for both...

We study the optimal consumption and portfolio for an agent maximizing the expected utility of his intertemporal consumption in a financial market with: (i) a riskless asset, (ii) a stock, (iii) a bond as a derivative on the stochastic interest rate, and (iv) a longevity bond whose coupons are...

In a recent article Davidson, Lawrence and Wilson propose a model showing that, in the presence of distortionary taxations and goods of different quality, tax evasion can be an optimal device. Here, we show that this result, although quite interesting, cannot be generalised to a framework where...

A longevity bond pays coupons which are proportional to the survival rate of a given population. In such a way the longevity risk becomes hedgeable on the financial market. In our model there are: (i) a longevity bond as a derivative on the population survival rate, (ii) a bond as a derivative...