Optimal Buy/Sell Rules for Correlated Random Walks

Allaart, Pieter C.; Monticino, Michael

doi:10.1017/s0021900200003934

Cited by 4 publications

(2 citation statements)

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“…Along with the main dynamic programming method some alternative approaches were proposed, for example, the linear programming technique (see, e.g., recent works [8,17]). Concerning optimal stopping in 336 E. Gordienko and A. Novikov the non-Markovian case there were some new results dealing with some particular classes of processes (see, e.g., [1,2,20]). Concerning optimal stopping in 336 E. Gordienko and A. Novikov the non-Markovian case there were some new results dealing with some particular classes of processes (see, e.g., [1,2,20]).…”

Section: Introductionmentioning

confidence: 99%

Characterizations of Optimal Policies in a General Stopping Problem and Stability Estimating

Gordienko¹,

Novikov²

2014

Prob. Eng. Inf. Sci.

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We consider an optimal stopping problem for a general discrete-time process X 1 , X 2 , . . . , Xn, . . . on a common measurable space. Stopping at time n (n = 1, 2, . . . ) yields a reward Rn(X 1 , . . . , Xn) ≥ 0, while if we do not stop, we pay cn(X 1 , . . . , Xn) ≥ 0 and keep observing the process. The problem is to characterize all the optimal stopping times τ , i.e., such that maximize the mean net gain:cn(X 1 , . . . , Xn)).We propose a new simple approach to stopping problems which allows to obtain not only sufficient, but also necessary conditions of optimality in some natural classes of (randomized) stopping rules.In the particular case of Markov sequence X 1 , X 2 , . . . we estimate the stability of the optimal stopping problem under perturbations of transition probabilities.

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Section: Introductionmentioning

confidence: 99%

Characterizations of Optimal Policies in a General Stopping Problem and Stability Estimating

Gordienko¹,

Novikov²

2014

Prob. Eng. Inf. Sci.

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“…In addition to binomial tree processes, discrete-time processes 652 S. C. P. YAM ET AL. exhibiting momentum have also been proposed in the existing literature as a model of stock price processes; for example, Allaart (2004) used a correlated random walk to model a stock price process and looked for the optimal selling time so as to maximize the expected discounted return. Under the same model, Allaart and Monticino (2008) considered a multiple buy/sell trading strategy to maximize the expected value of total return. The intention of the present paper is not to argue which processes we should use to model the stock price process.…”

Section: Introductionmentioning

confidence: 99%

Two Rationales Behind the ‘Buy-And-Hold or Sell-At-Once’ Strategy

2009

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The trading strategy of 'buy-and-hold for superior stock and sell-at-once for inferior stock', as suggested by conventional wisdom, has long been prevalent in Wall Street. In this paper, two rationales are provided to support this trading strategy from a purely mathematical standpoint. Adopting the standard binomial tree model (or CRR model for short, as first introduced in Cox, Ross and Rubinstein (1979)) to model the stock price dynamics, we look for the optimal stock selling rule(s) so as to maximize (i) the chance that an investor can sell a stock precisely at its ultimate highest price over a fixed investment horizon [0, T ]; and (ii) the expected ratio of the selling price of a stock to its ultimate highest price over [0, T ]. We show that both problems have exactly the same optimal solution which can literally be interpreted as 'buy-and-hold or sell-at-once' depending on the value of p (the going-up probability of the stock price at each step): when p > 1 2 , selling the stock at the last time step N is the optimal selling strategy; when p = 1 2 , a selling time is optimal if the stock is sold either at the last time step or at the time step when the stock price reaches its running maximum price; and when p < 1 2 , time 0, i.e. selling the stock at once, is the unique optimal selling time.

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