A review on drawdown risk measures and their implications for risk management
As highlighted by the recent market turmoil following COVID‐19, markets can experience
significant retracements or drawdowns. While these recent market moves have definitely …
significant retracements or drawdowns. While these recent market moves have definitely …
Speed and duration of drawdown under general Markov models
We propose an efficient computational method based on continuous-time Markov chain
(CTMC) approximation to compute the distributions of the speed and duration of drawdown …
(CTMC) approximation to compute the distributions of the speed and duration of drawdown …
Optimal stopping problems for maxima and minima in models with asymmetric information
PV Gapeev, L Li - Stochastics, 2022 - Taylor & Francis
We derive closed-form solutions to optimal stopping problems related to the pricing of
perpetual American withdrawable standard and lookback put and call options in an …
perpetual American withdrawable standard and lookback put and call options in an …
Optimal double stopping problems for maxima and minima of geometric Brownian motions
We present closed-form solutions to some double optimal stopping problems with payoffs
representing linear functions of the running maxima and minima of a geometric Brownian …
representing linear functions of the running maxima and minima of a geometric Brownian …
Perpetual American standard and lookback options with event risk and asymmetric information
PV Gapeev, L Li - SIAM Journal on Financial Mathematics, 2022 - SIAM
We derive closed-form solutions to the perpetual American standard and floating-strike
lookback put and call options in an extension of the Black--Merton--Scholes model with …
lookback put and call options in an extension of the Black--Merton--Scholes model with …
Discounted optimal stopping problems for maxima of geometric Brownian motions with switching payoffs
We present closed-form solutions to some discounted optimal stopping problems for the
running maximum of a geometric Brownian motion with payoffs switching according to the …
running maximum of a geometric Brownian motion with payoffs switching according to the …
Discounted optimal stopping problems in first-passage time models with random thresholds
PV Gapeev, H Al Motairi - Journal of Applied Probability, 2022 - cambridge.org
We derive closed-form solutions to some discounted optimal stopping problems related to
the perpetual American cancellable dividend-paying put and call option pricing problems in …
the perpetual American cancellable dividend-paying put and call option pricing problems in …
Perpetual American double lookback options on drawdowns and drawups with floating strikes
PV Gapeev - Methodology and Computing in Applied Probability, 2022 - Springer
We present closed-form solutions to the problems of pricing of the perpetual American
double lookback put and call options on the maximum drawdown and the maximum drawup …
double lookback put and call options on the maximum drawdown and the maximum drawup …
Drawdowns of diffusions
P Salminen, P Vallois - arXiv preprint arXiv:2411.18374, 2024 - arxiv.org
In this paper we give excursion theoretical proofs of Lehoczky's formula (in an extended form
allowing a lower bound for the underlying diffusion) for the joint distribution of the first …
allowing a lower bound for the underlying diffusion) for the joint distribution of the first …
Optimal stopping problems for running minima with positive discounting rates
PV Gapeev - Statistics & Probability Letters, 2020 - Elsevier
We present analytic solutions to some optimal stopping problems for the running minimum of
a geometric Brownian motion with exponential positive discounting rates. The proof is based …
a geometric Brownian motion with exponential positive discounting rates. The proof is based …