当前抵押贷款证券化产品定价方法主要是现金流贴现取平均的方式,其本质是一种风险中性定价,忽视了不同投资者的风险态度在资产定价中的决定作用。本文运用Hodges and Neuberger(1989)提出的效用无差别定价原理,提出抵押贷款证券化衍生...当前抵押贷款证券化产品定价方法主要是现金流贴现取平均的方式,其本质是一种风险中性定价,忽视了不同投资者的风险态度在资产定价中的决定作用。本文运用Hodges and Neuberger(1989)提出的效用无差别定价原理,提出抵押贷款证券化衍生产品定价的一种新的方法。假设投资者具有对数消费效用,本文得到了易于实现的抵押贷款证券化产品定价计算公式,给出了Monte Carlo数值计算方法和应用举例,并进行了比较静态分析。展开更多
In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is model...In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is modeled as a geometric Brownian motion with drift being a two-state Markov chain. Based on observations of asset prices, investors want to detect the change points of price trends as accurately as possible, so that they can make the decision to buy. Using filtering techniques and stochastic analysis, we will develop the optimal boundary at which investors implement their decisions when the posterior probability process reaches a certain threshold.展开更多
In this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T], where the stock price is modelled by a geometric Brownian motion an...In this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T], where the stock price is modelled by a geometric Brownian motion and the ＇closeness＇ is measured by the relative error of the stock price to its highest price over [0, T]. More precisely, we want to optimize the expression：V^＊=sup 0≤τ≤T E[Vτ/MT],where （Vt）t≥0 is a geometric Drownian motion with constant drift α and constant volatility σ 〉 0, Mt = max Vs 0≤a〈t is the running maximum of the stock price, and the supremum is taken over all possible stopping times 0 ≤ τ≤T adapted to the natural filtration （Ft）t≥0 of the stock price. The above problem has been considered by Shiryacv, Xu and Zhou （2008） and Du Toit and Peskir （2009）. In this paper we provide an independent proof that when α=1/ 2 σ^2 , a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the 1 2 moment when the stock price hits its maximum price so far. Besides, when α 〉1/2σ^2 , selling the stock at the terminal time T is the unique optimal selling strategy. Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping pr of a stopping time τ to the optimal stopping strategy arisen in the classical ＂Secretary Problem＂.展开更多
To solve the selling problem which is resembled to the buying problem in [1], in this paper we solve the problem of determining the optimal time to sell a property in a location the drift of the asset drops from a hig...To solve the selling problem which is resembled to the buying problem in [1], in this paper we solve the problem of determining the optimal time to sell a property in a location the drift of the asset drops from a high value to a smaller one at some random change-point. This change-point is not directly observable for the investor, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. The asset price is modeled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time and thus, we model the drift as a two-state Markov chain. Using filtering and martingale techniques, stochastic analysis transform measurement, we reduce the problem to a one-dimensional optimal stopping problem. We also establish the optimal boundary at which the investor should liquidate the asset when the price process hit the boundary at first time.展开更多
In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and th...In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.展开更多
Among a variety of adaptive designs, stage-wise design, especially, two-stage design is an important one because patient responses are not available immediately but are available in batches or intermittently in some s...Among a variety of adaptive designs, stage-wise design, especially, two-stage design is an important one because patient responses are not available immediately but are available in batches or intermittently in some situations. In this paper, by Bayesian method, the general formula of asymptotical optimal worth is given, meanwhile the length of some optimal designs at first stage concerning two-stage trials in several important cases has been obtained.展开更多
文摘当前抵押贷款证券化产品定价方法主要是现金流贴现取平均的方式,其本质是一种风险中性定价,忽视了不同投资者的风险态度在资产定价中的决定作用。本文运用Hodges and Neuberger(1989)提出的效用无差别定价原理,提出抵押贷款证券化衍生产品定价的一种新的方法。假设投资者具有对数消费效用,本文得到了易于实现的抵押贷款证券化产品定价计算公式,给出了Monte Carlo数值计算方法和应用举例,并进行了比较静态分析。
文摘In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is modeled as a geometric Brownian motion with drift being a two-state Markov chain. Based on observations of asset prices, investors want to detect the change points of price trends as accurately as possible, so that they can make the decision to buy. Using filtering techniques and stochastic analysis, we will develop the optimal boundary at which investors implement their decisions when the posterior probability process reaches a certain threshold.
基金supported by the Hong Kong RGC GRF 502909The Hong Kong Polytechnic University Internal Grant APC0D+1 种基金The Hong Kong Polytechnic University Collaborative Research Grant G-YH96supported by an internal grant of code 201109176016 from the University of Hong Kong
文摘In this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T], where the stock price is modelled by a geometric Brownian motion and the ＇closeness＇ is measured by the relative error of the stock price to its highest price over [0, T]. More precisely, we want to optimize the expression：V^＊=sup 0≤τ≤T E[Vτ/MT],where （Vt）t≥0 is a geometric Drownian motion with constant drift α and constant volatility σ 〉 0, Mt = max Vs 0≤a〈t is the running maximum of the stock price, and the supremum is taken over all possible stopping times 0 ≤ τ≤T adapted to the natural filtration （Ft）t≥0 of the stock price. The above problem has been considered by Shiryacv, Xu and Zhou （2008） and Du Toit and Peskir （2009）. In this paper we provide an independent proof that when α=1/ 2 σ^2 , a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the 1 2 moment when the stock price hits its maximum price so far. Besides, when α 〉1/2σ^2 , selling the stock at the terminal time T is the unique optimal selling strategy. Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping pr of a stopping time τ to the optimal stopping strategy arisen in the classical ＂Secretary Problem＂.
文摘To solve the selling problem which is resembled to the buying problem in [1], in this paper we solve the problem of determining the optimal time to sell a property in a location the drift of the asset drops from a high value to a smaller one at some random change-point. This change-point is not directly observable for the investor, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. The asset price is modeled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time and thus, we model the drift as a two-state Markov chain. Using filtering and martingale techniques, stochastic analysis transform measurement, we reduce the problem to a one-dimensional optimal stopping problem. We also establish the optimal boundary at which the investor should liquidate the asset when the price process hit the boundary at first time.
文摘In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.
基金the National Natural Science Foundation of China (Grant No.10271001).
文摘Among a variety of adaptive designs, stage-wise design, especially, two-stage design is an important one because patient responses are not available immediately but are available in batches or intermittently in some situations. In this paper, by Bayesian method, the general formula of asymptotical optimal worth is given, meanwhile the length of some optimal designs at first stage concerning two-stage trials in several important cases has been obtained.
