Related papers: Optimal longevity of a dynasty

Ergodicity economics is a new branch of economic theory that notes the conceptual difference between time averages and expectation values, which coincide only for ergodic observables. It postulates that individual agents maximise the time…

In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…

In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the decision-maker. If the decision-maker at time t=0 can commit his/her…

In this paper, we study the finite-horizon problem of an economic agent's optimal consumption, investment, and job-switching decisions. The key new feature of our model is that the job-switching cost is time-varying. This extension leads to…

This paper extends Xing's (2023abcd) optimal growth models of catching-up economies from the case of production function switching to that of economic structure switching and argues how a country develops its economy by endogenous…

In this paper, we study economic dynamics in a standard overlapping generations model without production. In particular, using numerical methods, we obtain a necessary and sufficient condition for the existence of a topological chaos. This…

Rationality is often related to optimal decision making. Humans are known to be bounded rational agents. However, recent advances in computing, and other scientific and technical fields along with large amount of data have led to a feeling…

The tragedy of the commons has traditionally been framed as a problem of resource overuse driven by self-interested exploitation. In contrast, growing empirical evidence shows that insufficient use or abandonment of natural resources, known…

I examine global dynamics in a monetary model with overlapping generations of finite-horizon agents and a binding lower bound on nominal interest rates. Debt targeting rules exacerbate the possibility of self-fulfilling liquidity traps, for…

The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control problems with state constraints of the Bolza type from the monograph of L. Cesari…

We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. The human capital dynamics of each agent is described by a stochastic multiplicative process which,…

In this paper we study the dynamics and ergodic theory of certain economic models which are implicitly defined. We consider 1-dimensional and 2-dimensional overlapping generations models, a cash-in-advance model, heterogeneous markets and a…

Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their performance often deteriorates sharply in long-horizon tasks, exhibiting systematic breakdown beyond certain scales. Conventional explanations primarily…

We consider a biological population whose environment varies periodically in time, exhibiting two very different "seasons" : one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we…

Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is…

In this paper, we consider discrete-time infinite horizon problems of optimal control to a terminal set of states. These are the problems that are often taken as the starting point for adaptive dynamic programming. Under very general…

While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…

This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The…

This article is concerned with stability and performance of controlled stochastic processes under receding horizon policies. We carry out a systematic study of methods to guarantee stability under receding horizon policies via appropriate…

It has long been hypothesized that operating close to the critical state is beneficial for natural and artificial systems. We test this hypothesis by evolving foraging agents controlled by neural networks that can change the system's…