Related papers: Optimal longevity of a dynasty
We propose a new measure for eternal inflation, based on search optimization and first-passage statistics. This work builds on the dynamical selection mechanism for vacua based on search optimization proposed recently by the author and…
This paper studies long term investing by an investor that maximizes either expected utility from terminal wealth or from consumption. We introduce the concepts of a generalized stochastic discount factor (SDF) and of the minimum price to…
This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both…
Opportunities such as higher education can promote intergenerational mobility, leading individuals to achieve levels of socioeconomic status above that of their parents. We develop a dynamic model for allocating such opportunities in a…
We study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint…
We introduce a highly stylized, yet non trivial model of the economy, with a public and private sector coupled through a wealth tax and a redistribution policy. The model can be fully solved analytically, and allows one to address the…
We present the theoretical analysis and proofs of a recently developed algorithm that allows for optimal planning over long and infinite horizons for achieving multiple independent tasks that are partially observable and evolve over time.
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
How long a technological civilization remains active, and what determines whether it collapses or persists, is a central question for both projecting humanity's future and assessing the prevalence of detectable intelligence in the galaxy.…
This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and…
We study an optimal investment and consumption problem over a finite-time horizon, in which an individual invests in a risk-free asset and a risky asset, and evaluate utility using a general utility function that exhibits loss aversion with…
A decision-maker periodically acquires information about a changing state, controlling both the timing and content of updates. I characterize optimal policies using a decomposition of the dynamic problem into optimal stopping and static…
We consider the optimal dynamics in the infinite population evolution models with general symmetric fitness landscape. The search of optimal evolution trajectories are complicated due to sharp transitions (like shock waves) in evolution…
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…
It has long been hypothesized that operating close to the critical state is beneficial for natural, artificial and their evolutionary systems. We put this hypothesis to test in a system of evolving foraging agents controlled by neural…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
This paper combines a canonical epidemiology model of disease dynamics with government policy of lockdown and testing, and agents' decision to social distance in order to avoid getting infected. The model is calibrated with data on deaths…
In this paper, we consider how to construct the optimal solutions for a general discrete time infinite horizon optimal control problem. We establish necessary and sufficient conditions for optimality in the sense of a modified optimality…
We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…