Optimal Stopping Time, Consumption, Labour, and Portfolio Decision for a Pension Scheme

31 Pages Posted: 11 May 2019

See all articles by Francesco Menoncin

Francesco Menoncin

University of Brescia - Department of Economics

Sergio Vergalli

University of Brescia - Department of Economics; Fondazione Eni Enrico Mattei (FEEM), Milan

Date Written: April 22, 2019

Abstract

In this work we solve in a closed form the problem of an agent who wants to optimise the inter-temporal utility of both his consumption and leisure by choosing: (i) the optimal inter-temporal consumption, (ii) the optimal inter-temporal labour supply, (iii) the optimal share of wealth to invest in a risky asset, and (iv) the optimal retirement age. The wage of the agent is assumed to be stochastic and correlated with the risky asset on the financial market. The problem is split into two sub-problems: the optimal consumption, labour, and portfolio problem is solved first, and then the optimal stopping time is approached. The martingale method is used for the first problem, and it allows to solve it for any value of the stopping time which is just considered as a stochastic variable. The problem of the agent is solved by assuming that after retirement he received a utility that is proportional to the remaining human capital. Finally, a numerical simulation is presented for showing the behaviour over time of the optimal solution.

Keywords: Optimal Stopping Time, Retirement Choice, Labour Supply, Asset Allocation, Mortality Risk

JEL Classification: C61, D15, G11, J22

Suggested Citation

Menoncin, Francesco and Vergalli, Sergio, Optimal Stopping Time, Consumption, Labour, and Portfolio Decision for a Pension Scheme (April 22, 2019). FEEM Working Paper No. 9.2019, Available at SSRN: https://ssrn.com/abstract=3386083 or http://dx.doi.org/10.2139/ssrn.3386083

Francesco Menoncin

University of Brescia - Department of Economics ( email )

Via San Faustino 74B
Brescia, 25122
Italy
0039-0302988806 (Phone)
0039-0302988837 (Fax)

HOME PAGE: http://www.eco.unibs.it/~menoncin/

Sergio Vergalli (Contact Author)

University of Brescia - Department of Economics ( email )

Via San Faustino 74B
Brescia, 25122
Italy

Fondazione Eni Enrico Mattei (FEEM), Milan ( email )

Corso Magenta 63
20123 Milan
Italy

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