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In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at the origin, dividends give rise…
This paper addresses the continuous-time portfolio selection problem under generalized disappointment aversion (GDA). The implicit definition of the certainty equivalent within GDA preferences introduces time inconsistency to this problem.…
Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
We consider 2-player stochastic games with perfectly observed actions, and study the limit, as the discount factor goes to one, of the equilibrium payoffs set. In the usual setup where current states are observed by the players, we show…
In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
Dynamically distributed inflation is a common mechanism used to guide a blockchain's staking rate towards a desired equilibrium between network security and token liquidity. However, the high sensitivity of the annual percentage yield to…
We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e. the dividend rate can never decrease. We solve the resulting two-dimensional…
A simple generative model of a foraging society generates significant wealth inequalities from identical agents on an equal opportunity landscape. These inequalities arise in both equilibrium and non-equilibrium regimes with some societies…
This paper considers an insurance company that faces two key constraints: a ratcheting dividend constraint and an irreversible reinsurance constraint. The company allocates part of its reserve to pay dividends to its shareholders while…
Researchers often turn to block randomization to increase the precision of their inference or due to practical considerations, such as in multisite trials. However, if the number of treatments under consideration is large it might not be…
We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their…
"Rational bubble", as introduced by the famous paper on money by Samuelson (1958), means speculation backed by nothing. The large subsequent rational bubble literature has identified attaching bubbles to dividend-paying assets in a natural…
Liquid simulations for computer animation often avoid simulating the air phase to reduce computational costs and ensure good conditioning of the linear systems required to enforce incompressibility. However, this free surface assumption…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
Inflationary models, especially those with plateau-type potentials, are consistent with the cosmological data, but inflation itself does not resolve the initial singularity. This singularity is resolved, for example, by the idea of the…
We propose an aggregate notion of non-transferable utility (NTU) stability for decentralized matching markets with fixed prices, where market clearing is achieved through one-sided money burning, which can be interpreted as waiting. Agents…