arXiv research

We consider a Bayesian financial market with one bond and one stock where the aim is to maximize the expected power utility from terminal wealth. The solution of this problem is known, however there are some conjectures in the literature about the long-term behavior of the optimal strategy. In this paper we prove now t…

Combines absolute and relative wealth in portfolio optimization with power utility functions.

Greedy algorithm optimizes consumption habits with power utility.

The paper proves an equilibrium in a limited stock market participation model with power utilities.

We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is power utility. We provide a heuristic and a rigorous derivation of the asymptotic ex…

We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in term…

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framewor…

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a nove…

Paper tackles time inconsistency in portfolio management with stochastic volatility and power utility.

We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity pr…

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strate…

Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative…

Study optimal strategies for insurer's dividends, investments, and liabilities.

Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems…

The paper studies price impacts in asset liquidation markets.

Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…

We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor…

Study robust utility maximization with uncertain continuous semimartingales.

We consider the problem of maximizing expected power utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in Shreve and Soner [Ann. Appl. Probab. 4 (1994) 609-692]. Similar to Kallsen and Muhle-Karbe [Ann. Appl. Probab. 20 (2010) 1341-1358], we der…

We discuss the turnpike property for optimal investment and consumption problems. We find there exists a threshold value that determines the turnpike property for investment policy. The threshold value only depends on the Sharpe ratio, the riskless interest rate and the discount rate. We show that if utilities behave a…

The paper addresses optimal control in modern tontines with bequest preferences, showing a linear investment strategy.

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximiza…

Photovoltaic systems have been widely deployed in recent times to meet the increased electricity demand as an environmental-friendly energy source. The major challenge for integrating photovoltaic systems in power systems is the unpredictability of the solar power generated. In this paper, we analyze the impact of havi…

The aim of this paper is to study the fast computation of the lower and upper bounds on the value function for utility maximization under the Heston stochastic volatility model with general utility functions. It is well known there is a closed form solution of the HJB equation for power utility due to its homothetic pr…

We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…

Study examines how liquidity constraints impact optimal retirement decisions.

This work derives an approximate analytical single period solution of the portfolio choice problem for the power utility function. It is possible to do so if we consider that the asset returns follow a multivariate normal distribution. It is shown in the literature that the log-normal distribution seems to be a good pr…

We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit form, which can be compared and interpreted. This paper continues our previous wor…

We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic programming, we characterize the value function with a backward stochastic differential equ…

Two deep learning algorithms solve utility maximisation problems in finance.

We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an $R^d$-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial…

We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we…

Study Epstein-Zin preferences in mean field portfolio games, proving unique equilibria.

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on R converges to the exponential utility. Under a …

Solves optimal control for trading multiple mean-reverting assets.

Study optimal trading strategies with expert signals in a hidden Gaussian drift market.

Adversaries with multiple antennas can fool deep learning modulators more effectively.

The paper examines utility maximization in markets with hidden Gaussian drift, finding restrictions on model parameters.

In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this incomplete market context the problem of maximization of expected utility from terminal…

Paper develops duality theory for robust utility maximization in continuous time.

This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional averag…

Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of power utility-based prices and hedging strategies can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. In order to avoid the introduction of an addition…

The paper analyzes a private likelihood-ratio test for frequency tables under differential privacy constraints.

We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space o…

We study a portfolio selection problem in a continuous-time Itô-Markov additive market with prices of financial assets described by Markov additive processes which combine Lévy processes and regime switching models. Thus the model takes into account two sources of risk: the jump diffusion risk and the regime switching …

This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constra…

We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the…

In the general framework of a semimartingale financial model and a utility function $U$ defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a ``small'' number of random endowments. We show that this linear approximation has some important qualitative …