skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Optimal consumption of multiple goods in incomplete markets
We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.  more » « less
Award ID(s):
1600307
PAR ID:
10079820
Author(s) / Creator(s):
Date Published:
Journal Name:
Journal of Applied Probability
Volume:
55
Issue:
3
ISSN:
0021-9002
Page Range / eLocation ID:
810 - 822
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, Journal of Applied Probability)
    Abstract We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk and of the finiteness of both primal and dual value functions. 
    more » « less
  2. ; (, Mathematical Finance)
    We investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish. 
    more » « less
  3. ; ; ; (, IEEE Conference Decision and Control)
    null (Ed.)
    A new stochastic control methodology is introduced for distributed control, motivated by the goal of creating virtual energy storage from flexible electric loads, i.e. Demand Dispatch. In recent work, the authors have introduced Kullback- Leibler-Quadratic (KLQ) optimal control as a stochastic control methodology for Markovian models. This paper develops KLQ theory and demonstrates its applicability to demand dispatch. In one formulation of the design, the grid balancing authority simply broadcasts the desired tracking signal, and the hetero-geneous population of loads ramps power consumption up and down to accurately track the signal. Analysis of the Lagrangian dual of the KLQ optimization problem leads to a menu of solution options, and expressions of the gradient and Hessian suitable for Monte-Carlo-based optimization. Numerical results illustrate these theoretical results. 
    more » « less
  4. ; ; ; ; ; (, IEEE)
    As vehicular communication networks embrace metaverse beyond 5G/6G systems, the rich content update via the least interfered subchannel of the optimal frequency band in a hybrid band vehicle to everything (V2X) setting emerges as a challenging optimization problem. We model this problem as a tradeoff between multi-band VR/AR devices attempting to perform metaverse scenes and environmental updates to metaverse roadside units (MRSUs) while minimizing energy consumption. Due to the computational hardness of this optimization, we formulate an opportunistic band selection problem using a multi-armed bandit (MAB) that provides a good quality solution in real-time without computationally burdening the already stretched augmented/virtual reality (AR/VR) units acting as transmitting nodes. The opportunistic use of scheduling rich content updates at traffic signals and stand-still scenarios maps well with the formulated bandit problem. We propose a Dual-Objective Minimax Optimal Stochastic Strategy (DOMOSS) as a natural solution to this problem. Through extensive computer-based simulations, we demonstrate the effectiveness of our proposal in contrast to baselines and comparable solutions. We also verify the quality of our solution and the convergence of the proposed strategy. 
    more » « less
  5. ; ; ; (, Operations Research)
    The objective of this paper is to study the optimal consumption and portfolio choice problem of risk-controlled investors who strive to maximize total expected discounted utility of both consumption and terminal wealth. Risk is measured by the variance of terminal wealth, which introduces a nonlinear function of the expected value into the control problem. The control problem presented is no longer a standard stochastic control problem but rather, a mean field-type control problem. The optimal portfolio and consumption rules are obtained explicitly. Numerical results shed light on the importance of controlling variance risk. The optimal investment policy is nonmyopic, and consumption is not sacrificed. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email