A Note on COVID-19 Instigated Maximum Drawdown in Islamic Markets versus Conventional Counterparts,

The objective of the continuous time mean-variance model is to minimize the variance (risk) of an investment portfolio with a given mean at the terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this problem, we consider to minimize the variances of the investment portfolio in the multi-time state. The advantage of this multi-time state mean-variance model is the minimization of the risk of the investment portfolio within the investment period. To obtain the optimal strategy of the model, we introduce a sequence of Riccati equations, which are connected by jump boundary conditions. In addition, we establish the relationships between the means and variances in the multi-time state mean-variance model. Furthermore, we use an example to verify that the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.

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A Refined Measure of Conditional Maximum Drawdown

SSRN Electronic Journal ◽

10.2139/ssrn.3337828 ◽

2019 ◽

Author(s):

Damiano Rossello

Keyword(s):

Conditional Maximum ◽

Maximum Drawdown

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On the maximum drawdown of a Brownian motion

Journal of Applied Probability ◽

10.1239/jap/1077134674 ◽

2004 ◽

Vol 41 (1) ◽

pp. 147-161 ◽

Cited By ~ 81

Author(s):

Malik Magdon-Ismail ◽

Amir F. Atiya ◽

Amrit Pratap ◽

Yaser S. Abu-Mostafa

Keyword(s):

Brownian Motion ◽

Random Process ◽

Infinite Series ◽

Series Representation ◽

Expected Value ◽

Square Root ◽

Brownian Motion With Drift ◽

Negative Drift ◽

Analytic Expression ◽

Maximum Drawdown

The maximum drawdown at time T of a random process on [0,T] can be defined informally as the largest drop from a peak to a trough. In this paper, we investigate the behaviour of this statistic for a Brownian motion with drift. In particular, we give an infinite series representation of its distribution and consider its expected value. When the drift is zero, we give an analytic expression for the expected value, and for nonzero drift, we give an infinite series representation. For all cases, we compute the limiting (T → ∞) behaviour, which can be logarithmic (for positive drift), square root (for zero drift) or linear (for negative drift).

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