The Robust Merton Problem of an Ambiguity Averse Investor

带学习的模糊金融市场中的均值-方差优化

Mean-Variance Optimization in Ambiguous Financial Markets with Learning

针对多资产Black-Scholes市场中漂移未知且存在模型模糊性的问题，提出一种考虑平滑模糊厌恶的均值-方差准则，通过新颖方法得到允许学习的动态最优投资策略，并数值分析了参数影响。

Robust Portfolios and Weak Incentives in Long-Run Investments

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage-free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not a…

Portfolio Optimization with Nondominated Priors and Unbounded Parameters

We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertainty on the parameters of both mean and volatility. We take that the investor has logarithmic utility function, and solve the corresponding utility maximization problem explicitly. To the best of our knowledge, this is the first work on utility maximization with unbounded mean and …

具有投资组合约束和随机环境的鲁棒最优投资与消费策略

Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment

本文研究随机扩散市场中受投资与消费约束的鲁棒连续时间投资—消费问题，结合随机 HJBI 方程、BSDE 和 BMO 鞅理论刻画最优策略、价值函数与忽视不确定性的效用损失。

Portfolio optimization in the case of an asset with a given liquidation time distribution

Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses in this case we need to develop new methods. One of the steps moving the theory towards practical needs is to take into account the time lag of the liquidation of an illiquid asset. This task became especially significant for the practitioners in the time of the global financial crises. …

Robust Optimization of Credit Portfolios

We introduce a dynamic credit portfolio framework where optimal investment strategies are robust against misspecifications of the reference credit model. The risk-averse investor models his fear of credit risk misspecification by considering a set of plausible alternatives whose expected log likelihood ratios are penalized. We provide an explicit characterization of the optimal robust bond investment strategy, in terms of default state dependent value functions associated with the max-min robust optimization criterion. The value functions can be obtained as the solutions of a recursive system …

Optimal Sharing Rule for a Household with a Portfolio Management Problem

We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption and final wealth. Each agent has different utility function and discount factor. An explicit formulation for the optimal consumptions and portfolio can be obtained in the case of a complete market. The problem is shown to be equivalent to maximizing three different utilities separately with separate initial wealths. We study a numerical example where the mar…

Closed-form portfolio optimization under GARCH models

This paper develops the first closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. We obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston st…

条件风险价值（CVaR）约束下的动态投资组合优化

Dynamic Portfolio Optimization under CVaR Constraints

本文针对CVaR约束下的连续时间动态投资组合优化问题，提出对偶嵌套二分-黄金分割搜索算法，证明策略收敛性，数值实验揭示风险约束紧时的状态依赖策略及非交易风险、价格冲击的影响。

Designing an Optimal Portfolio for Iran's Stock Market with Genetic Algorithm using Neural Network Prediction of Risk and Return Stocks

Optimal capital allocation between different assets is an important financial problem, which is generally framed as the portfolio optimization problem. General models include the single-period and multi-period cases. The traditional Mean-Variance model introduced by Harry Markowitz has been the basis of many models used to solve the portfolio optimization problem. The overall goal is to achieve the highest return and lowest risk in portfolio optimization problems. In this paper, we will present an optimal portfolio based the Markowitz Mean-Variance-Skewness with weight constraints model for sh…

Portfolio Optimization in Affine Models with Markov Switching

We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this aim we apply Merton's approach, as we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains we first derive the HJB equations, which in our case correspond to a system of coupled non-line…

Portfolio Optimization under Habit Formation

The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of consumption at any given time depends only on the amount consumed at that time. However, it is both theoretically and empirically reasonable that an individuals utility of consumption would depend on past consumption history. Economists term this "Habit Formation". We introduce a new formulation of habit formation which allows non-addictive consumption patt…

跳跃-扩散框架下一类新型比例投资组合保险策略的最优设计研究

On the optimal design of a new class of proportional portfolio insurance strategies in a jump-diffusion framework

本文研究跳跃-扩散框架下比例投资组合保险（PPI）策略的最优投资问题，通过S型效用函数和推广的鞅方法解决市场不完全性下的缺口风险，最大化损失厌恶型代理人的终端财富期望效用。