The maximum drawdown of the Brownian motion
نویسندگان
چکیده
where X ( t ) represents the equity curve of the trading system or fund. The maximum drawdown MDD is the most widespread risk measure among money managers and hedge funds. It is often preferred over some of the other risk measures because of the tight relationship between large drawdowns and fund redemptions. Also, a large drawdown can even indicate the start of a deterioration of an otherwise successful trading system, for example due to a market regime switch.
منابع مشابه
Drawdowns Preceding Rallies in the Brownian Motion Model
We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability that a drawdown of a units precedes a rally of b units. We apply this result to examine stock market c...
متن کاملOccupation Times, Drawdowns, and Drawups for One-dimensional Regular Diffusions
The drawdown process of a one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown precedes a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are appli...
متن کاملThe effect of various conductivity and viscosity models considering Brownian motion on nanofluids mixed convection flow and heat transfer
In this paper the effect of using various models for conductivity and viscosity considering Brownian motion of nanoparticles is investigated. This study is numerically conducted inside a cavity full of Water-Al2O3 nanofluid at the case of mixed convection heat transfer. The effect of some parameters such as the nanoparticle volume fraction, Rayleigh, Richardson and Reynolds numbers has been ex...
متن کاملFormulas for stopped diffusion processes with stopping times based on drawdowns and drawups
This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that a drawdown of size a precedes a drawup of size b and vice versa. The results are applied to several ...
متن کاملOn the Maximum Drawdown of a Brownian Motion
If X(t) is a random process on [0, T ], the maximum drawdown at time T , D̄(T ), is defined by D̄(T ) = sup t∈[0,T ] [ sup s∈[0,t] X(s)−X(t) ] . Informally, this is the largest drop from a peak to a bottom. In this paper, we investigate the behavior of this statistic for a Brownian motion with drift. In particular, we give an infinite series representation of its distribution, and consider its ex...
متن کامل