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10 results on '"Al-Foraih, Mishari"'

1. Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach

Author

Al-Foraih, Mishari, Pospíšil, Jan, and Vives, Josep

Subjects
Quantitative Finance - Mathematical Finance, 60G22, 91G20, 91G60
Abstract

Using Malliavin calculus techniques we obtain formulas for computing Greeks under different rough Volterra stochastic volatility models. In particular we obtain formulas for rough versions of Stein-Stein, SABR and Bergomi models and numerically demonstrate the convergence.

Published
2023

2. Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency

Author

Es-Sebaiy, Khalifa, Alazemi, Fares, and Al-Foraih, Mishari

Subjects
Mathematics - Statistics Theory, Mathematics - Probability
Abstract

This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $\theta$, for a Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of $\theta$, namely $\widetilde{\theta}_{n}\coloneqq {1}/{\left(\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2}\right)}$, and $\widehat{\theta}_{n}\coloneqq -{\sum_{i=1}^{n} X_{t_{i-1}}\left(X_{t_{i}}-X_{t_{i-1}}\right)}/{\left(\Delta_{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2}\right)}$, respectively, where $ t_{i} = i \Delta_{n}$, $ i=0,1,\ldots, n $, $\Delta_{n}\rightarrow 0$. We provide Wasserstein bounds in central limit theorem for $\widetilde{\theta}_{n}$ and $\widehat{\theta}_{n}$., Comment: arXiv admin note: text overlap with arXiv:2102.04810

Published
2022

4. Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters

Author

Alsenafi, Abdulaziz, Al-Foraih, Mishari, and Es-Sebaiy, Khalifa

Subjects
Mathematics - Probability, Mathematics - Statistics Theory
Abstract

Let $B^{a,b}:=\{B_t^{a,b},t\geq0\}$ be a weighted fractional Brownian motion of parameters $a>-1$, $|b|<1$, $|b|0$ of the weighted fractional Ornstein-Uhlenbeck process $X:=\{X_t,t\geq0\}$ defined by $X_0=0; \ dX_t=\theta X_tdt+dB_t^{a,b}$. In this work, we provide least squares-type estimators for $\theta$ based continuous-time and discrete-time observations of $X$. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all $(a,b)$ such that $a>-1$, $|b|<1$, $|b|

Published
2020

5. Applications in optimization and investment lag problem

Author

Al-Foraih, Mishari Najeeb, Johnson, Paul, and Duck, Peter

Subjects
519.3, Optimization, Real Options valuations, Dynamic programming
Abstract

This thesis studies two optimization problems: the optimization of a staffing policy assuming non stationary Poisson demand, and exponential travel and job times, and the optimization of investment decisions with an investment lag. In the staffing policy optimization, we solve a novel time-dynamic Hamilton-Jacobi-Bellman equation that models jobs as a Poisson jump process. The model gives the employer the flexibility to control the number of staff hired by two factors: the cost of hiring and the effect of delay. We have solved the optimal staffing policy problem using different approaches, which are compared. We produce accurate numerical results for different parameters, and discuss the advantages and disadvantages of each approach. Moreover, we have solved a staffing problem for a national utility company, using a standard linear programming approach, which is compared with our methods. In addition to the Poisson jump process, we extend the model to treat a continuous job model, and two locations model that is extendible to a larger network problem. In the investment lag problem, we use a mixture of numerical methods including finite difference and body fitted co-ordinates to form a robust and stable numerical scheme which is applied to solve the investment lag problem for a geometric Brownian motion presented in the paper by Bar-Ilan and Strange (1996). The problem is to calculate the optimal price to invest in a project that have a time lag period between the decision to invest and production, and the optimal price to mothball the project. The method presented in this thesis is more flexible as we compare it with the previous results, and solves the problem for different stochastic processes, such as Cox-Ingersoll-Ross model, which does not have analytic solution.

Published
2015

9. Investment Lags: A Numerical Approach

Author

Al-Foraih, Mishari, Johnson, Paul, Duck, Peter, Al-Foraih, Mishari, Johnson, Paul, and Duck, Peter

Abstract

In this paper we use a mixture of numerical methods including finite difference and body fitted co-ordinates to form a robust stable numerical scheme to solve the investment lag model presented in the paper by Bar-Ilan and Strange (1996). This allows us to apply our methodology to models with different stochastic processes that does not have analytic solutions.

10. Optimal Staffing Policy: A Service System with Stochastic Travel Times

Author

Al-Foraih, Mishari, Johnson, Paul, Evatt, Geoff, Duck, Peter, Al-Foraih, Mishari, Johnson, Paul, Evatt, Geoff, and Duck, Peter

Abstract

Private sector operators of response services such as ambulance, fire or police etc. are often regulated with targets on the distribution of response times, which may result in inefficient over staffing to ensure those targets are met. In this paper, we use a network chain of M=M=K queues to model the arrival and completion of jobs on the system so that quantities such as the expected total time waiting for all jobs can be calculated. The Markov nature enables us to evoke the Hamilton Jacobi Bellman equation (HJB) principle to optimize the required number of staff whilst still meeting targets.

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