Volume 30, Issue 1

There is no method of predicting the price of an option other than hedging strategies such as the binomial hedging strategy, the Black–Scholes hedging strategy and others. We will study these two basic hedging strategies in terms of their feasibility, and we will see that the Black–Scholes hedging strategy is not feasible because this strategy demands instantaneously rebuilding the replicating portfolio. Consequently, the real world prices of the options are not relevant at all with the Black–Scholes hedging strategy! We will suitably redefine the binomial hedging strategy so that it will be practically useful and present other feasible and generally more effective hedging strategies with some of them practically useful for options with no tradable underlying assets. Finally, we will mention some open questions related to the above.

In this paper, we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients to estimate mean curves of components. This procedure has the advantage of estimating component functions with important local characteristics such as discontinuities, spikes and oscillations for example, due the features of wavelet basis expansion of functions. Simulation studies were done to evaluate the performance of the proposed method, and its results are compared with a spline-based method. An application on the so-called Tecator dataset is also provided.

In this paper, under some suitable conditions, we prove existence of a strong solution and uniqueness for the perturbed stochastic differential equations with reflected boundary (PSDERB), that is, { x ⁢ ( t ) = x ⁢ ( 0 ) + ∫ 0 t σ ⁢ ( s , x ⁢ ( s ) ) ⁢ d B ⁢ ( s ) + ∫ 0 t b ⁢ ( s , x ⁢ ( s ) ) ⁢ d s + α ⁢ ( t ) ⁢ H ⁢ ( max 0 ≤ u ≤ t ⁡ x ⁢ ( u ) ) + β ⁢ ( t ) ⁢ L t 0 ⁢ ( x ) , x ⁢ ( t ) ≥ 0 for all ⁢ t ≥ 0 , \left\{\begin{aligned} {}x(t)&=x(0)+\int_{0}^{t}\sigma(s,x(s))\,dB(s)+\int_{0}^{t}b(s,x(s))\,ds+\alpha(t)H\bigl{(}\max_{0\leq u\leq t}x(u)\bigr{)}+\beta(t)L_{t}^{0}(x),\\ x(t)&\geq 0\quad\text{for all}\ t\geq 0,\end{aligned}\right. where 𝐻 is a continuous R-valued function, σ , b , α \sigma,b,\alpha and 𝛽 are measurable functions, L t 0 L_{t}^{0} denotes a local time at point zero for the time of the semi-martingale 𝑥.

The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude. The periodicity of the frequency components is also thought to affect the convergence of these parameters. In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal. Under the high-frequency sampling setting, we provide the frequency components’ consistency and asymptotic normality. It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl. 29 (2023), 1, 1–32]. The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic. In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components. Further, the result of the study, that is, the convergence rate of the frequency is ( n ⁢ h ) 3 \sqrt{(nh)^{3}} , also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, J. Math. Comput. Sci. 11 (2021), 5, 6433–6443], which mentioned ( n ⁢ h ) 3 ⁢ h \sqrt{(nh)^{3}h} . The proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household.

We establish theoretical properties of the solution to a two-variance-driven interest rate model with super-linear coefficient terms. Since this model is not tractable analytically, we construct an implementable numerical method to approximate it and prove the finite-time strong convergence theory under the local Lipschitz condition. Finally, we provide simulation examples to demonstrate the theoretical results.

The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.

This paper proposes the nonparametric asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system, after perturbation of arrival distribution to evaluate the proximity of the complex GI/M/1 system, where GI is a unknown general distribution. The class of generalized gamma (GG) kernels is considered because of its several interesting properties and flexibility. A simulation for several models illustrates the performance of the GG asymmetric kernel estimators in the study of strong stability of the PH/M/1, by computing the variation distance and the stability error.