Contingent-claim Valuation of a Closed-end Fund: Models and Implications

2009 ◽  
Vol 17 (4) ◽  
pp. 43-74
Author(s):  
Chaehwan Won ◽  
Sangho Yi
Keyword(s):  
Stochastic Processes ◽  
Mutual Funds ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Optimal Timing ◽  
Contingent Claim ◽  
Investment Strategies ◽  
Valuation Model ◽  
Contingent Claim Valuation ◽  
Closed End Funds

In this paper, we develop various valuation models for closed-end mutual funds under different sets of stochastic processes for the underlying assets. Since we used different stochastic processes from previous literature, it was possible to derive more interesting implications regarding investment strategies, discount puzzles of the funds, and valuation models. In particular, by utilizing Brownian motions and optimal stopping time framework, we succeeded in developing more realistic valuation model, which indicates that we can understand more easily about decision makings regarding optimal timing of reorganization from the closed-end funds to open-ended funds, optimal timing of trading of closed-end funds to realize maximum profits, and optimal design of closed-end fund structure.

Optimal Stopping Under General Dependence Conditions

1983 ◽  
Vol 26 (3) ◽  
pp. 260-266
Author(s):  
M. Longnecker
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Random Variables ◽  
Stopping Times ◽  
Dependence Conditions ◽  
Series Type

AbstractLet {Xn} be a sequence of random variables, not necessarily independent or identically distributed, put and Mn =max0≤k≤n|Sk|. Effective bounds on in terms of assumed bounds on , are used to identify conditions under which an extended-valued stopping time τ exists. That is these inequalities are used to guarantee the existence of the stopping time τ such that E(ST/aτ) = supt ∈ T∞ E(|Sτ|/at), where T∞ denotes the class of randomized extended-valued stopping times based on S1, S2, … and {an} is a sequence of constants. Specific applications to stochastic processes of the time series type are considered.

OPTIMAL TIMING OF THE ANNUITY PURCHASE: COMBINED STOCHASTIC CONTROL AND OPTIMAL STOPPING PROBLEM

2006 ◽  
Vol 09 (02) ◽  
pp. 151-170 ◽  
Author(s):  
GABRIELE STABILE
Keyword(s):  
Stochastic Control ◽  
Optimal Stopping ◽  
Optimal Timing ◽  
Investment Strategies ◽  
Optimal Controls ◽  
Optimal Stopping Problem ◽  
Power Utility ◽  
Individual Subject ◽  
Force Of Mortality ◽  
The Individual

The paper examines the optimal annuitization time and the optimal consumption/investment strategies for a retired individual subject to a constant force of mortality in an all-or-nothing framework. We allow for a different utility of consumption before and after annuitization. For a general family of preferences we characterize the value function and the optimal controls of the resulting combined stochastic control and optimal stopping problem. Assuming power utility functions we obtain explicit solutions. We show that if the individual evaluates the consumption flow and the annuity payments stream in the same way, then, depending on the parameters of the economy, the annuity is purchased at retirement or never. In the case when the individual is more risk averse in the annuity assessment, it is optimal to defer the annuitization until her wealth reaches a threshold, and such threshold depends on the parameters of the economy.

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time

On wald-type optimal stopping for Brownian motion

1997 ◽  
Vol 34 (1) ◽  
pp. 66-73 ◽  
Author(s):  
S. E. Graversen ◽  
G. Peškir
Keyword(s):  
Brownian Motion ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Maximal Inequality ◽  
Stopping Times ◽  
Standard Brownian Motion ◽  
Square Root ◽  
Real Analysis ◽  
Optimal Stopping Problems ◽  
Wald's Identity

The solution is presented to all optimal stopping problems of the form supτE(G(|Β τ |) – cτ), where is standard Brownian motion and the supremum is taken over all stopping times τ for B with finite expectation, while the map G : ℝ+ → ℝ satisfies for some being given and fixed. The optimal stopping time is shown to be the hitting time by the reflecting Brownian motion of the set of all (approximate) maximum points of the map . The method of proof relies upon Wald's identity for Brownian motion and simple real analysis arguments. A simple proof of the Dubins–Jacka–Schwarz–Shepp–Shiryaev (square root of two) maximal inequality for randomly stopped Brownian motion is given as an application.

scholarly journals Valuations and Decisions of Investing in Corporate Social Responsibility: A Real Options Viewpoint

2018 ◽  
Vol 10 (10) ◽  
pp. 3532 ◽  
Author(s):  
Kuo-Jung Lee
Keyword(s):  
Corporate Social Responsibility ◽  
Social Responsibility ◽  
Real Options ◽  
Optimal Strategies ◽  
Optimal Timing ◽  
Valuation Model ◽  
Real Options Approach ◽  
Corporate Social ◽  
Options Value

Corporate social responsibility (CSR) implementation could raise corporate reputations and benefit long-term development. Studying the effects of CRS on corporate valuation is essential. However, studies on the valuation of CSR are limited, particularly studies involving a dynamic model for valuing CSR. This study applies a real options approach to derive the company valuation of CSR investments, CSR options value, and the optimal timing for implementing CSR. This study elucidates the value of CSR and the decision to invest in CSR. Specifically, the value of CSR options facilitates determining whether to invest in CSR, and the optimal threshold for implementing CSR indicates explicitly when to invest in CSR. In addition, numerical analyses and results are demonstrated to verify the established model. This is the first and novel attempt to consider the valuation model and optimal strategies of CSR investments using the methods of real options.

scholarly journals On some problems of the optimal stopping of stable stochastic processes

1972 ◽  
Vol 12 (1) ◽  
pp. 173-179
Author(s):  
V. Mackevičius
Keyword(s):  
Stochastic Processes ◽  
Optimal Stopping

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: В. Мацкявичюс. О некоторых задачах оптимальной остановки устойчивых случайных процессов V. Mackevičius. Apie kai kuriuos stabilių atsitiktinių procesų optimalaus sustabdymo uždavinius

Optimal stopping and maximal inequalities for geometric Brownian motion

1998 ◽  
Vol 35 (04) ◽  
pp. 856-872 ◽  
Author(s):  
S. E. Graversen ◽  
G. Peskir
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Optimal Stopping ◽  
Moving Boundary ◽  
Stopping Time ◽  
Practical Interest ◽  
Maximal Inequality ◽  
Geometric Brownian Motion ◽  
Stopping Times ◽  
Image Position

Explicit formulas are found for the payoff and the optimal stopping strategy of the optimal stopping problem supτ E (max0≤t≤τ X t − c τ), where X = (X t ) t≥0 is geometric Brownian motion with drift μ and volatility σ > 0, and the supremum is taken over all stopping times for X. The payoff is shown to be finite, if and only if μ < 0. The optimal stopping time is given by τ* = inf {t > 0 | X t = g * (max0≤t≤s X s )} where s ↦ g *(s) is the maximal solution of the (nonlinear) differential equation under the condition 0 < g(s) < s, where Δ = 1 − 2μ / σ2 and K = Δ σ2 / 2c. The estimate is established g *(s) ∼ ((Δ − 1) / K Δ)1 / Δ s 1−1/Δ as s → ∞. Applying these results we prove the following maximal inequality: where τ may be any stopping time for X. This extends the well-known identity E (sup t>0 X t ) = 1 − (σ 2 / 2 μ) and is shown to be sharp. The method of proof relies upon a smooth pasting guess (for the Stephan problem with moving boundary) and the Itô–Tanaka formula (being applied two-dimensionally). The key point and main novelty in our approach is the maximality principle for the moving boundary (the optimal stopping boundary is the maximal solution of the differential equation obtained by a smooth pasting guess). We think that this principle is by itself of theoretical and practical interest.

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