A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper solves a utility-based hedging problem with quadratic costs.
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…
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…
A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating an…
The Mean-Variance Criterion is equivalent to Second-order Stochastic Dominance under symmetric Elliptical distributions.
Investment and consumption strategy optimized under uncertain conditions.
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model, and provides two linear approximations for the utility indifference price. The key tool is a probabilistic representation for the utility indifference price by the solution of a functional differential equation…
New results on financial equilibria in markets with general semimartingales.
Investor optimizes utility in a market with endogenous pricing.
Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
Inspired by complexity and diversity of biological neurons, our group proposed quadratic neurons by replacing the inner product in current artificial neurons with a quadratic operation on input data, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power o…
Study optimal investment and consumption in incomplete markets with nonlinear expectations.
This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equation…
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 present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman eq…
Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.
Prompted by a recent experiment by Victor Haghani and Richard Dewey, this note generalises the Kelly strategy (optimal for simple investment games with log utility) to a large class of practical utility functions and including the effect of extraneous wealth. A counterintuitive result is proved : for any continuous, co…
We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete market model among a group of agents whose preference is characterized by cash invariant time-consistent monetary utilities. An assumption of "smallness" type is shown to be sufficient for existence and uniqueness. In par…
Study utility indifference pricing with delayed investment information in a Bachelier model.
We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a…
The paper calculates how fast optimal investment strategies approach CRRA strategies in stochastic factor models.
Gradient descent dynamics in quadratic regression models are analyzed, revealing five phases: monotonic, catapult, periodic, chaotic, and divergent.
Investment strategy optimization from discrete to continuous models.
The paper studies deformations and confluences of singularities in meromorphic connections and quadratic differentials.
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (…
In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed a…
Investigates optimal consumption and investment strategies with constraints in incomplete markets.
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the op…
The paper finds optimal strategies for hedging in incomplete markets using derivatives.
Study on price formation among investors with exponential utility and liabilities.
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility. Our approach is based on martingale methods which rely on recent results on the e…
Study of a game with multiple players and common shocks using probabilistic methods.
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this p…
This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum …
New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.
This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded framework, we extend our analysis to the more challenging unbounded case. Our methodolo…
Deep learning solves dynamic programming with recursive utility.
In this paper, we construct the utility-based optimal hedging strategy for a European-type option in the Almgren-Chriss model with temporary price impact. The main mathematical challenge of this work stems from the degeneracy of the second order terms and the quadratic growth of the first order terms in the associated …
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…
We study the dynamics of the exponential utility indifference value process C(B;α) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B;α) is (the first component of) the unique solution of a backward stochastic differential equation with a quadratic generator and o…
This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an analytical approach that employs martingale extraction and involves finding the …
The paper solves a portfolio selection problem in incomplete markets by balancing utility and risk.
Develops asset pricing models with mean field game theory for heterogeneous agents.
The paper solves TIC LQ control problems using stochastic differential games.
New algorithm tackles stochastic optimization with inequality constraints.
Study on price formation in financial markets with a single default event.
Paper solves portfolio problem using improved stochastic methods.
Proposes r2SGLD for efficient constrained exploration in non-convex learning.