Related papers: Short-horizon Duesenberry Equilibrium
This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero…
We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential L\'evy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic…
We investigate stochastic differential games of optimal trading comprising a finite population. There are market frictions in the present framework, which take the form of stochastic permanent and temporary price impacts. Moreover,…
An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of…
We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes.…
We study Markowitz's mean-variance portfolio selection problem in a continuous-time Black-Scholes market with different borrowing and saving rates. The associated Hamilton-Jacobi-Bellman equation is fully nonlinear. Using a delicate partial…
Various formulations of counterfactual general equilibrium in economies -- systems of actors manipulating economic goods -- are logically and mathematically analyzed. Evenly-rotating economies are systems whose evolution is stable, steady,…
This paper studies an optimal investment-reinsurance problem for an insurer (she) under the Cram\'er--Lundberg model with monotone mean--variance (MMV) criterion. At any time, the insurer can purchase reinsurance (or acquire new business)…
A growing body of empirical evidence suggests that the dynamics of wealth within a population tends to be non-ergodic, even after rescaling the individual wealth with the population average. Despite these discoveries, the way in which…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process,…
We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…
We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process.…
We propose a general strategy for solving nonlinear integro-differential evolution problems with periodic boundary conditions, where no direct maximum/minimum principle is available. This is motivated by the study of recent macroscopic…
We discuss a possibility of deriving an H-theorem for nonlinear discrete time evolution equation that describes random wealth exchanges. In such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a…
This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new…
We study competitive equilibria in the classic Shapley-Shubik assignment model with indivisible goods and unit-demand buyers, with budget constraints: buyers can specify a maximum price they are willing to pay for each item, beyond which…
We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local)…
We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic…
The war of attrition with two-sided asymmetric information is a foundational model in political economy, yet it generically admits a continuum of perfect Bayesian equilibria. This paper characterizes the sources of equilibrium multiplicity.…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…