基于动态VaR约束与随机波动率模型的最优投资策略

研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题. 假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产, 风险资产的价格过程由Stein-Stein随机波动率模型刻画. 同时, 投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法, 得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式; 并通过理论分析和数值算例, 阐述了动态VaR约束与随机波动率对最优投资策略的影响.     

Vasicek利率与Heston模型下的最优投资和再保险

本文主要研究Vasicek随机利率模型下保险公司的最优投资与再保险问题.假设保险公司的盈余过程由带漂移的布朗运动来描述,保险公司通过购买比例再保险来转移索赔风险;同时,将财富投资于由一种无风险资产与一种风险资产组成的金融市场,其中,利率期限结构服从Vasicek利率模型,且风险资产价格过程满足Heston随机波动率模型.利用动态规划原理及变量替换的方法,得到了指数效用下最优投资与再保险策略的显示表达式,并给出数值例子分析了主要模型参数对最优策略的影响.     

跳扩散市场投资组合研究

研究了连续时间动态均值-方差投资组合选择问题.假设风险资产价格服从跳跃-扩散过程且具有卖空约束.投资者的目标是在给定期望终止时刻财富条件下,最小化终止时刻财富的方差.通过求解模型相应的Hamilton-Jacobi-Bellmen方程,得到了最优投资策略及有效前沿的显示解.结果显示,风险资产的卖空约束及价格过程的跳跃因素对最优投资策略及有效前沿的是不可忽略的.     

利用传染模型对含有对手风险的信用证券定价(英文)

本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.     

最小化破产概率的保险人鲁棒投资再保险策略研究

在模型不确定条件下,研究以破产概率最小化为目标的模糊厌恶型保险公司的最优投资再保险问题. 假设保险公司可投资于一种风险资产,也可购买比例再保险. 分别考虑风险资产的价格过程服从随机波动率模型和非随机波动率模型的两种情况,根据动态规划原理建立相应的HJB方程,得到保险公司的最优鲁棒投资再保险策略和价值函数的解析解. 最后,通过数值模拟分析了各模型参数对最优策略和价值函数的影响.     

Heston模型下基于HARA效用准则的资产-负债管理策略

研究了Heston随机波动率模型下带有负债过程的动态投资组合问题,并且假设风险资产价格过程满足Heston随机波动率模型,负债过程服从带漂移的布朗运动.金融市场由一种无风险资产和一种风险资产所构成.首先,应用动态规划原理得到相应值函数所满足的HJB方程.然后,假设投资者对风险的偏好程度满足双曲绝对风险厌恶(HARA)效用函数,并应用Legendre变换法和分离变量法得到在HARA效用函数下最优投资策略的显示解.最后,给出数值算例分析部分市场参数对最优投资策略的影响.     

随机利率下跳-扩散过程的产量保险定价模型

本文研究了农产品价格为一般的跳-扩散模型,随机跳部分为复合Poisson过程,并假设远期利率服从HJM模型,利用测度变换技巧,给出了合同的在此模型下的解析解.     

内部信息者的最小亏损风险策略

在一定的假设条件下,利用扩大信息流方法解决了跳扩散环境下内部信息者的最小亏损风险策略问题.首先构建了内部信息者最小亏损风险策略模型,证明了内部信息市场的完备性.然后利用风险资产价格的Markov性和鞅表示定理得到了线性损失函数下的最小亏损风险最优策略和相应的价值函数.     

Ornstein-Uhlenbeck模型下保险与再保险的均衡保险投资分析

本文构建保险公司和再保险公司的比例再保险与投资组合微分博弈模型,研究两公司基于加权终期财富效用最大化的均衡决策问题.假设保险公司的资本盈余过程为复合Poisson风险跳过程,为降低赔付风险,保险公司可以向再保险公司购买比例再保险.两个公司都可以投资于风险资产满足Ornstein-Uhlenbeck随机模型的金融市场,优化资本管理.在保险公司和再保险公司的绝对风险厌恶指数不随财富数量而变化的假设下,利用博弈论和动态规划原理,得到了两公司的Nash均衡比例再保险和投资组合策略的解析表达式.给出了均衡保险与投资存在的必要条件,对均衡条件下的再保险供需关系进行了分析.     

Markov调节中基于时滞和相依风险模型的最优再保险与投资

本文研究保险公司在Markov调节下基于时滞及相依风险模型的最优再保险与最优投资问题,其中市场被划分为有限个状态,一些重要的参数随着市场状态的转换而变化.假设保险公司的盈余过程由复合Poisson过程描述,而风险资产的价格过程由几何跳扩散模型刻画,并且假设这两个跳过程是相依的.以最大化终端财富值的均值-方差效用为目标,...     

随机利率下期权定价

本文在随机利率的基础上,考虑股票价格过程和利率过程分别为扩散过程和Ito过程,并且在相关的假设下,运用鞅方法推导出欧式期权价值过程所满足的微分方程;以及利率满足一种特殊方程时,运用最优停止的鞅方法,得到了随机利率下美式期权的价格和最优停时.     

Emergent dynamics of the first‐order stochastic Cucker‐Smale model and application to finance

In this paper, we study stochastic aggregation properties of the financial model for the N‐asset price process whose dynamics is modeled by the weakly geometric Brownian motions with stochastic drifts. For the temporal evolution of stochastic components of drift coefficients, we employ a stochastic first‐order Cucker‐Smale model with additive noises. The asset price processes are weakly interacting via the stochastic components of drift coefficients. For the aggregation estimates, we use the macro‐micro decomposition of the fluctuations around the average process and show that the fluctuations around the average value satisfies a practical aggregation estimate over a time‐independent symmetric network topology so that we can control the differences of drift coefficients by tuning the coupling strength. We provide numerical examples and compare them with our analytical results. We also discuss some financial implications of our proposed model.     

Moments of the asset price for the Barndorff-Nielsen and Shephard model

In this paper, we derive closed-form formulas for moments of the asset price in the Barndorff-Nielsen and Shephard (BN–S) stochastic volatility model. We also present similar results where the market is driven by a BN–S-type stochastic process. It is shown that in both cases the results depend on the cumulant transform of the background driving Lévy process for the models. In this paper, we have also obtain various approximate expressions for the expected value of the square-root process for the shifted asset price with respect to the BN–S model.     

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.     

Robust consumption-investment problems with random market coefficients

We consider consumption-investment problems in a financial market with general random coefficients where the market price of risk process is unknown. The investor tries to maximize his expected utility under the worst-case parameter configuration. To solve robust consumption-investment problems, we make use of stochastic Bellman?CIsaac equations. These equations can be explicitly solved for power, exponential and logarithmic utility. This enables us to characterize a robust optimal consumption-investment strategy and a worst-case market price of risk process in terms of the solution of a backward stochastic differential equation.     

Pricing catastrophe options with counterparty credit risk in a reduced form model

In this paper, we study the price of catastrophe options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model. We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.     

Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations

For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent γ?>?1/2, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise comparison theorem. An application to option price estimation is given.     

The optimal harvesting problem under price uncertainty

In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor, with finite and infinite time horizon. We assume that harvest is restricted to mature trees older than a certain age and that growth and natural mortality after maturity are neglected. We use stochastic dynamic programming techniques to characterize the optimal policy and we model price using a geometric Brownian motion and an Ornstein–Uhlenbeck process. In the first case we completely characterize the optimal policy for all possible choices of the parameters. In the second case we provide sufficient conditions, based on explicit expressions for reservation prices, assuring that harvesting everything available is optimal. In addition, for the Ornstein–Uhlenbeck case we propose a policy based on a reservation price that performs well in numerical simulations. In both cases we solve the problem for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state.     

Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree

In this paper, we present a natural mathematical framework to model trader behavior as a continuous time discrete event process, and derive stochastic differential equations for aggregate behavior and price dynamics by passing to diffusion limits. In particular, we model extraneous, value, momentum and hedge traders. Through analysis and numerical simulation we explore some of the effects these trading strategies have on price dynamics.     

Stochastic processes adapted by neural networks with application to climate, energy, and finance

Local climate parameters may naturally effect the price of many commodities and their derivatives. Therefore we propose a joint framework for stochastic modeling of climate and commodity prices. In our setting, a stable Levy process is drift augmented to a generalized SDE. The related nonlinear function on the state space typically exhibits deterministic chaos. Additionally, a neural network adapts the parameters of the stable process such that the latter produces increasingly optimal differences between simulated output and observed data. Thus we propose a novel method of “intelligent” calibration of the stochastic process, using learning neural networks in order to dynamically adapt the parameters of the stochastic model.