Related papers: Optimal Consumption under a Habit-Formation Constr…
There is no known explicit global closed form solution for the standard income fluctuation problem with a borrowing constraint and where wealth accumulates with a constant interest rate $r$. Using a continuous time formulation, I derive an…
We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…
In consequential domains, it is often impossible to compel individuals to take treatment, so that optimal policy rules are merely suggestions in the presence of human non-adherence to treatment recommendations. We study personalized…
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation…
We explore intertemporal preferences that are recursive and account for local intertemporal substitution. First, we establish a rigorous foundation for these preferences and analyze their properties. Next, we examine the associated optimal…
We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is an extension of the optimal…
We assume that an agent's rate of consumption is {\it ratcheted}; that is, it forms a non-decreasing process. Given the rate of consumption, we act as financial advisers and find the optimal investment strategy for the agent who wishes to…
We reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market;…
Selective labels are a common feature of consequential decision-making applications, referring to the lack of observed outcomes under one of the possible decisions. This paper reports work in progress on learning decision policies in the…
We extend the lifecycle model (LCM) of consumption over a random horizon (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt…
This paper presents a systematic study on gap-dependent sample complexity in offline reinforcement learning. Prior work showed when the density ratio between an optimal policy and the behavior policy is upper bounded (the optimal policy…
We present a model of credit card profitability, assuming that the card-holder always pays the full outstanding balance. The motivation for the model is to calculate an optimal credit limit, which requires an expression for the expected…
We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of…
We develop a duality theory for the problem of maximising expected lifetime utility from inter-temporal wealth over an infinite horizon, under the minimal no-arbitrage assumption of No Unbounded Profit with Bounded Risk (NUPBR). We use only…
The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as halo effects, that…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
The decision to annuitize wealth in retirement planning has become increasingly complex due to rising longevity risk and changing retirement patterns, including increased labor force participation at older ages. While an extensive…
In this paper, on the line e.g. of [COW00]) we investigate a model with habit formation and two types of substitute goods. Such family of models, even in the case of 1 good, are difficult to study since their utility function is not concave…
Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is…
We study a n-player and mean-field portfolio optimization problem under relative performance concerns with non-zero volatility, for wealth and consumption. The consistency assumption defining forward relative performance processes leads to…