Optimal Retirement Under Partial Information

The optimal retirement decision is an optimal stopping problem when retirement is irreversible. We investigate the optimal consumption, investment, and retirement decisions when the mean return of a risky asset is unobservable and is estimated by filtering from historical prices. To ensure nonnegativity of the consumption rate and the borrowing constraints on the wealth process of the representative agent, we conduct our analysis using a duality approach. We link the dual problem to American option pricing with stochastic volatility and prove that the duality gap is closed. We then apply our theory to a hidden Markov model for regime-switching mean return with Bayesian learning. We fully characterize the existence and uniqueness of variational inequality in the dual optimal stopping problem, as well as the free boundary of the problem. An asymptotic closed-form solution is derived for optimal retirement timing by small-scale perturbation. We discuss the potential applications of the results to other partial-information settings.

Investment Decisions with Two-Factor Uncertainty

This paper considers investment problems in real options with non-homogeneous two-factor uncertainty. We derive some analytical properties of the resulting optimal stopping problem and present a finite difference algorithm to approximate the firm’s value function and optimal exercise boundary. An important message in our paper is that the frequently applied quasi-analytical approach underestimates the impact of uncertainty. This is caused by the fact that the quasi-analytical solution does not satisfy the partial differential equation that governs the value function. As a result, the quasi-analytical approach may wrongly advise to invest in a substantial part of the state space.

Methodological Remarks Regarding Optimal Stopping Tasks and the Implications for Sampling Biases

This paper investigates a type of optimal stopping problem where options are presented in sequence and, once an option has been rejected, it is impossible to go back to it. With previous research finding mixed results of undersampling and oversampling biases on these kinds of optimal stopping tasks, the question remaining is what causes people to sample too much or too little compared to models of optimality? In two pilot studies and a main study, we explored task features that could lead to over- versus undersampling on number-based tasks. We found that, regardless of task features, there were no significant differences in human sampling rate across conditions. Nevertheless, we observed differences in sampling biases across conditions due to varying sampling rates of the optimal model. Our optimal model, like most models used for this type of optimal stopping problem, requires that researchers specify the mean and variance of a theoretical distribution, from which the options are generated. We show that different ways of specifying this generating distribution can lead to different model sampling rates, and consequently, differences in sampling biases. This highlights that a correct specification of the generating distribution is critical when investigating sampling biases on optimal stopping tasks.

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

Reflected BSDEs when the obstacle is predictable and nonlinear optimal stopping problem

In the first part of this paper, we study RBSDEs in the case where the filtration is non-quasi-left-continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal stopping theory in the predictable setting, some tools from general theory of processes as the Mertens decomposition of predictable strong supermartingale. In the second part, we introduce an optimal stopping problem indexed by predictable stopping times with the nonlinear predictable [Formula: see text] expectation induced by an appropriate backward stochastic differential equation (BSDE). We establish some useful properties of [Formula: see text]-supremartingales. Moreover, we show the existence of an optimal predictable stopping time, and we characterize the predictable value function in terms of the first component of RBSDEs studied in the first part.

Equilibrium Allocations Under Alternative Waitlist Designs: Evidence From Deceased Donor Kidneys

Waitlists are often used to ration scarce resources, but the trade‐offs in designing these mechanisms depend on agents' preferences. We study equilibrium allocations under alternative designs for the deceased donor kidney waitlist. We model the decision to accept an organ or wait for a preferable one as an optimal stopping problem and estimate preferences using administrative data from the New York City area. Our estimates show that while some kidney types are desirable for all patients, there is substantial match‐specific heterogeneity in values. We then develop methods to evaluate alternative mechanisms, comparing their effects on patient welfare to an equivalent change in donor supply. Past reforms to the kidney waitlist primarily resulted in redistribution, with similar welfare and organ discard rates to the benchmark first‐come, first‐served mechanism. These mechanisms and other commonly studied theoretical benchmarks remain far from optimal. We design a mechanism that increases patient welfare by the equivalent of an 18.2% increase in donor supply.