Investment and consumption strategy for risk-averse agents with Epstein-Zin utility.
problem Optimal investment and consumption strategy for Epstein-Zin utility.
method Detailed introduction to Epstein-Zin utility, existence and uniqueness proof, verification argument.
result Existence and uniqueness of optimal solution for Epstein-Zin utility under certain parameter restrictions.
In a market with stochastic investment opportunities, we study an optimal consumption investment problem for an agent with recursive utility of Epstein-Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize…
Investigates stability of Epstein-Zin problem under market distortions.
problem Stability of Epstein-Zin problem in incomplete markets.
method Analyzes perturbations in returns and volatility, and interest rate; proves convergence of optimal solutions.
result Proves convergence of optimal consumption streams and value functions in the limit of model perturbations.
Study optimal healthcare spending under Epstein-Zin preferences for longevity.
problem Optimizing healthcare spending to extend longevity under Epstein-Zin preferences.
method Formulated Epstein-Zin utilities over a controllable random horizon using backward stochastic differential equations and HJB equations.
result Calibrated model accurately reflects actual mortality data and compares healthcare efficacy between countries.
Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
problem Optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
method Martingale optimal principle and quadratic BSDEs with exponential moment.
result Establishes optimal strategies for consumption and investment.
Study optimal consumption and investment for investors with Epstein-Zin preferences.
problem Optimal consumption and investment for investors with Epstein-Zin preferences in an incomplete market.
method Variational characterisation and direct method to prove existence of optimal policies.
result Existence and uniqueness of optimal consumption and investment policies.
Investigates optimal consumption and investment strategies with constraints in incomplete markets.
problem Optimal consumption and investment under constraints in incomplete markets.
method Characterizes optimal strategies via a quadratic BSDE, using martingale optimality criterion and Lyapunov functions.
result Obtains the verification theorem for optimal strategies in unbounded cases.
Paper shows equivalence between two dividend preference models.
problem Understanding investor and firm preferences for dividends.
method Formulated Epstein-Zin preference, proved equivalence with Maenhout's model.
result Robust dividend policy is equivalent to a threshold strategy based on surplus process.
Study optimal consumption and investment strategies with leverage constraints using Epstein-Zin utility.
problem Optimal portfolio choice under leverage constraints and Epstein-Zin utility.
method Established viscosity solution to HJB equation, demonstrated smoothness, characterized optimal strategies, derived explicit solutions.
result Explicit solutions for optimal consumption and investment strategies under leverage constraints.
Study Epstein-Zin preferences in mean field portfolio games, proving unique equilibria.
problem Analyzing portfolio games with Epstein-Zin preferences under non-Markovian conditions.
method Proves a one-to-one correspondence between Nash equilibria and BSDE solutions, using local stochastic maximum principle tailored to Epstein-Zin utility.
result Establishes uniqueness of equilibria in mean field portfolio games under Epstein-Zin preferences.
Paper solves investment and consumption problem with unknown risk, providing explicit solutions.
problem Solving consumption-investment problem with unknown market price of risk and terminal liability constraint.
method Introduced a coupled forward-backward stochastic differential equation (FBSDE) and provided an explicit solution.
result Explicit expressions for optimal investment strategy and value function derived.
This paper solves optimal investment-consumption problems for a risk-averse agent with special utility.
problem Optimal investment-consumption problem for a risk-averse agent with special utility.
method Introduced proper utility process and solved optimal investment-consumption problem.
result Existence and uniqueness of proper utility processes for a wide class of consumption streams.
Optimizes investment strategies for retirees with longevity risk.
problem Maximizing retirement savings under longevity risk for a group of investors.
method Analytic and numerical solutions for investment strategies in both discrete and continuous time models.
result Analytic formulae for optimal investment strategies in both discrete and continuous time models.
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…
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…
This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment proble…
In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We compute analytically the optimal investment-consumption strategy for a fund of n identical investors with homogeneous Epstein--Zin preferences, investing in the Black--Scholes mark…
Study optimizes insurance and investment strategies for risk-averse insurers under ambiguity.
problem Optimizing insurance and investment strategies for risk-averse insurers under ambiguity.
method Solves a coupled FBSDE to derive optimal strategies and value function.
result Optimal consumption, investment, and reinsurance strategies influenced by risk aversion and EIS.
Deep learning solves dynamic programming with recursive utility.
problem Challenges in solving high-dimensional discrete-time dynamic programming problems with recursive utility.
method Certainty Equivalent Learning (CEL) algorithm that learns certainty-equivalent value directly with neural networks.
result Accurate value and policy approximations in high-dimensional problems, comparable to VFI in some cases.
Study portfolio optimization with transaction costs and recursive preferences.
problem Optimizing portfolios under transaction costs and recursive preferences.
method Recursive preferences, transaction costs, and Merton investment-consumption problem.
result Characterized all parameter combinations for well-posedness of the problem.
The standard asset pricing models (the CCAPM and the Epstein-Zin non-expected utility model) counterintuitively predict that equilibrium asset prices can rise if the representative agent's risk aversion increases. If the income effect, which implies enhanced saving as a result of an increase in risk aversion, dominates…
CEFOL uses deep learning for dynamic programming with recursive utility.
problem Challenges in solving dynamic programming problems with recursive utility.
method Introduces a separate neural network for certainty equivalent, uses first-order optimality conditions to learn value and policy functions.
result CEFOL achieves high accuracy in learning value and policy functions, matching VFI benchmarks.
Study many-player investment-consumption games with power FPPs, finding market-risk preference affects consumption.
problem Investment and consumption optimization in a mean field competition setting.
method Solve many-player and mean field games using power FPPs, providing closed-form solutions.
result Market-risk relative consumption preference affects agent's consumption decisions.
Extends wealth tax neutrality framework to stochastic volatility and non-homothetic preferences.
problem Ensuring wealth taxes are neutral under various economic conditions.
method Extended Frøseth's neutrality framework to stochastic volatility and non-homothetic preferences, identified four channels of non-neutrality, and applied the framework to global minimum wealth taxes.
result Non-uniform assessment, general equilibrium effects, progressive thresholds, and endogenous labour supply can cause non-neutrality under CRRA preferences.
Investors adjust spending based on a social norm, spending less during losses and more during gains.
problem Managing spending and portfolio decisions while adhering to a social norm.
method Formulated a preference ordering with two CRRA preference orderings, solved analytically and numerically.
result Annual spending should be lower than expected financial return and procyclical, with spending cuts following losses.
We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold gr…
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
Solves four problems related to circle families in the plane.
problem Four basic problems of circle families in the plane.
method Solves all four basic problems of circle families in the plane.
result All four basic problems are solved.
Solves four problems related to sphere families in 3D space.
problem Four basic problems of sphere families in Euclidean 3-space.
method Solves all four basic problems of sphere families in Euclidean 3-space.
result All four basic problems are solved.
The paper solves optimal control problems for various convex sets using convex trigonometry.
problem Optimal control problems with 2D convex compact sets.
method Using convex trigonometry to derive extremals for various problems.
result Geodesics in multiple sub-Finsler problems are derived.
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…
This paper solves the Christoffel problem in hyperbolic space and its equivalent on spheres.
problem Prescribing curvatures for convex hypersurfaces in hyperbolic space.
method Proving a full rank theorem to establish the existence of solutions.
result Existence of solutions to the Christoffel problem and its equivalent Nirenberg-Kazdan-Warner problem on spheres.
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we anal…
Study proves only origin-centered spheres solve certain curvature problems.
problem Proving uniqueness of solutions to curvature problems.
method Using the Heintze-Karcher inequality, the study proves the uniqueness of smooth, strictly convex solutions to a class of Minkowski type problems.
result Only origin-centered spheres solve isotropic and Lp-Gaussian-Minkowski problems. MathChat uses LLM agents to solve challenging math problems through conversational problem-solving.
problem Solving math problems expressed in natural language.
method MathChat is a conversational framework combining an LLM agent and a user proxy agent for collaborative problem-solving.
result MathChat improves tool-using prompting methods by 6% on difficult math problems.
The paper solves a generalized Christoffel-Minkowski problem using a curvature flow.
problem Solving the (p,q)-Christoffel-Minkowski problem.
method Investigating the problem via an expanding curvature flow.
result Existence and uniqueness of smooth solutions to the (p,q)-Christoffel-Minkowski problem.
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
The paper explains how microlocal analysis solves geometric inverse problems.
problem Recovering geometric information from boundary measurements.
method Microlocal analysis applied to three inverse problems.
result Microlocal techniques solve specific inverse problems in Riemannian geometry.
Proves NP and co-NP status for knot core recognition in solid torus.
problem Determining if a knot is the core of a solid torus.
method Alternate proof and corollary of Hopf link recognition problem.
result Proves NP and co-NP status for solid torus core recognition problem.
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most exist…
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For ea…
We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric problems about (almost) complex structures, both algebraic and non-algebraic, about co…
New method solves generalized Minkowski problem for torsional rigidity.
problem Generalized Minkowski problem for torsional rigidity.
method Flow method
result Existence of solutions for general measures.
We present 27 problems encountered in automating the translation of movie/TV show subtitles. We categorize each problem in one of the three categories viz. problems directly related to textual translation, problems related to subtitle creation guidelines, and problems due to adaptability of machine translation (MT) eng…
Solves Brezis' first open problem on ball solutions.
problem Existence of solutions to Brezis-Nirenberg problem on a 3D ball.
method Building on sign-changing solutions to the Yamabe problem.
result Infinitely many sign-changing, nonradial solutions found.
Classical knot recognition problem solved in NP with exponential time algorithm.
problem Determining if a virtual knot is classical.
method Proved NP membership and provided an exponential time algorithm.
result Classical knot recognition problem is in NP.
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking or media memorability. In this article, we systematically review different types…