Optimal Retirement with Borrowing Constraints and Forced Unemployment Risk

In this paper, we study optimal retirement in a two-dimensional incomplete market caused by borrowing constraints and forced unemployment risk. We show that the two aspects jointly affect an individual’s optimal consumption, investment, and retirement strategies. In contrast to the complete market case, the endogenously determined wealth threshold for retirement is significantly affected by the two-dimensional market incompleteness, resulting in a lower wealth threshold. We also discuss a possible unemployment insurance scheme for the borrowing-constrained individual to respond to the shocks of forced unemployment

Optimal portfolio choice with path dependent labor income: the infinite horizon case

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agentreceives labor income which adjusts to financial market shocks in a path dependent way. Thispath-dependency is the novelty of the model, and leads to an infinite dimensional stochasticoptimal control problem. We solve the problem completely, and find explicitly the optimalcontrols in feedback form. This is possible because we are able to find an explicit solutionto the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if stateconstraints are present. To the best of our knowledge, this is the first infinite dimensionalgeneralization of Merton’s optimal portfolio problem for which explicit solutions can be found.The explicit solution allows us to study the properties of optimal strategies and discuss theirfinancial implications

Minimizing the Probability of Ruin in Exchange Rate Markets

The goal of this paper is to extend the results of Bayraktar and Young (2006) on minimizing an individual\u27s probability of lifetime ruin; i.e. the probability that the individual goes bankrupt before dying. We consider a scenario in which the individual is allowed to invest in both a domestic bank account and a foreign bank account, with the exchange rate between the two currencies being modeled by geometric Brownian motion. Additionally, we impose the restriction that the individual is not allowed to borrow money, and assume that the individual\u27s wealth is consumed at a constant rate. We derive formulas for the minimum probability of ruin as well as the individual\u27s optimal investment strategy. We also give a few numerical examples to illustrate these results

Wage Rigidity and Retirement in Optimal Portfolio Choice

We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite retirement time leads to a novel, two-stage infinite dimensional stochastic optimal control problem, which we fully solve obtaining explicitly the optimal controls in feedback form. This is possible as we find an explicit solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, which is an infinite dimensional PDE of parabolic type. The identification of the optimal feedbacks is more delicate than in arXiv:2002.00201 to the two-stage structure and to the presence of time-dependent state constraints, which appear to be new in the infinite dimensional stochastic control literature. The explicit solution allows us to study the properties of optimal strategies and discuss their implications for portfolio choice. Importantly, we discuss not only the optimal allocations for the case of labor income spanned by the traded assets, but also provide novel insights into the case in which wages are also driven by idiosyncratic shocks.Comment: 30 pages, 1 figur

Constrained Portfolio Choices in the Decumulation Phase of a Pension Plan

This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement. This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. The main goal is to find the optimal portfolio choice to be adopted by the retiree from retirement to annuitization time in a Black and Scholes financial market. We define and study the problem at two different complexity levels. In the first level (problem P1), we only require no short-selling. In the second level (problem P2), we add a constraint on the state variable, by imposing that the final fund cannot be lower than a certain guaranteed safety level. This implies, in particular, no ruin. The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We give a general result of existence and uniqueness of regular solutions for the Hamilton-Jacobi-Bellman equation and, in a special case, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application of the special case - when explicit solutions are available - ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement. This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. The main goal is to find the optimal portfolio choice to be adopted by the retiree from retirement to annuitization time in a Black and Scholes financial market. We define and study the problem at two different complexity levels. In the first level (problem P1), we only require no short-selling. In the second level (problem P2), we add a constraint on the state variable, by imposing that the final fund cannot be lower than a certain guaranteed safety level. This implies, in particular, no ruin. The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We give a general result of existence and uniqueness of regular solutions for the Hamilton-Jacobi-Bellman equation and, in a special case, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application of the special case - when explicit solutions are available - ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.Non-Refereed Working Papers / of national relevance onl

Unemployment Risks and Optimal Retirement in an Incomplete Market

We develop a new approach for solving the optimal retirement problem for an individual with an unhedgeable income risk. The income risk stems from a forced unemployment event, which occurs as an exponentially-distributed random shock. The optimal retirement problem is to determine an individual's optimal consumption and investment behaviors and optimal retirement time simultaneously. We introduce a new convex-duality approach for reformulating the original retirement problem and provide an iterative numerical method to solve it. Reasonably calibrated parameters say that our model can give an explanation for lower consumption and risky investment behaviors of individuals, and for relatively higher stock holdings of the poor. We also analyze the sensitivity of an individual's optimal behavior in changing her wealth level, investment opportunity, and the magnitude of preference for post-retirement leisure. Finally, we find that our model explains a counter-cyclical pattern of the number of unemployed job leavers

Simple Explicit Formula for Near-Optimal Stochastic Lifestyling

In lifecycle economics the Samuelson paradigm (Samuelson, 1969) states that optimal investment is in constant proportions out of lifetime wealth (composed of current savings and future income). It is well known that in the presence of credit constraints this paradigm no longer applies. Instead, optimal lifecycle investment gives rise to so-called stochastic lifestyling (Cairns et al., 2006), whereby for low levels of accumulated capital it is optimal to invest fully in stocks and then gradually switch to safer assets as the level of savings increases. In stochastic lifestyling not only does the ratio between risky and safe assets change but also the mix of risky assets varies over time. While the existing literature relies on complex numerical algorithms to quantify optimal lifestyling the present paper provides a simple formula that captures the main essence of the lifestyling effect with remarkable accuracy

Financial Structure and Economic Welfare: Applied General Equilibrium Development Economics

This review provides a common framework for researchers thinking about the next generation of micro-founded macro models of growth, inequality, and financial deepening, as well as direction for policy makers targeting microfinance programs to alleviate poverty. Topics include treatment of financial structure general equilibrium models: testing for as-if-complete markets or other financial underpinnings; examining dual-sector models with both a perfectly intermediated sector and a sector in financial autarky, as well as a second generation of these models that embeds information problems and other obstacles to trade; designing surveys to capture measures of income, investment/savings, and flow of funds; and aggregating individuals and households to the level of network, village, or national economy. The review concludes with new directions that overcome conceptual and computational limitations.National Science Foundation (U.S.)National Institutes of Health (U.S.)Templeton FoundationBill & Melinda Gates Foundatio