Author
Juan Pablo Rincón-Zapatero
Other affiliations: Complutense University of Madrid, University of Valladolid
Bio: Juan Pablo Rincón-Zapatero is an academic researcher from Charles III University of Madrid. The author has contributed to research in topics: Uniqueness & Bellman equation. The author has an hindex of 15, co-authored 47 publications receiving 740 citations. Previous affiliations of Juan Pablo Rincón-Zapatero include Complutense University of Madrid & University of Valladolid.
Papers
More filters
TL;DR: In this article, the authors studied the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns and provided sufficient conditions for the existence of solutions that can be applied to fairly general models.
Abstract: We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fixed point theorems. With appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions. Furthermore, the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models. It is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the Bellman operator.
98 citations
TL;DR: In this article, a continuous time dynamic pension funding model in a defined benefit plan of an employment system is considered, where benefits liabilities are random, given by a geometric Brownian process, and the main objective is to minimize both the contribution rate risk and the solvency risk.
Abstract: We consider a continuous time dynamic pension funding model in a defined benefit plan of an employment system. The benefits liabilities are random, given by a geometric Brownian process. Three different situations are studied regarding the investment decisions taken by the sponsoring employer: in the first, the fund is invested at a constant, risk-free rate of interest; in the second, the promoter invests in a portfolio with n risky assets and a risk-free security; finally, it is supposed that the rate of return is stochastic. Modelling the preferences of the manager such that the main objective is to minimize both the contribution rate risk and the solvency risk, we study cases where the optimal behavior leads to a spread method of funding.
80 citations
TL;DR: It is shown that the optimal portfolio depends linearly on the supplementary cost of the fund, plus an additional term due to the random evolution of benefits, and the efficient frontier is found.
61 citations
TL;DR: In this article, the authors consider a dynamic model of pension funding in a defined benefit plan of an employment system and determine the optimal funding behavior in this dynamic, stochastic framework.
Abstract: We consider a dynamic model of pension funding in a defined benefit plan of an employment system. The prior objective of the sponsor of the pension plan is the determination of the contribution rate amortizing the unfunded actuarial liability, in order to minimize the contribution rate risk and the solvency risk. To this end, the promoter invest in a portfolio with n risky assets and a risk-free security. The aim of this paper is to determine the optimal funding behavior in this dynamic, stochastic framework.
58 citations
TL;DR: This paper solves the optimal management of an aggregated pension fund of defined benefit type by means of optimal stochastic control techniques and analyzes the influence on the optimal solution of some of the parameters involved in the model.
57 citations
Cited by
More filters
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.
2,446 citations
Posted Content•
TL;DR: The Arrow-Pratt theory of risk aversion was shown to be isomorphic to the theory of optimal choice under risk in this paper, making possible the application of a large body of knowledge about risk aversion to precautionary saving.
Abstract: The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect
1,944 citations
499 citations