scholarly journals A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield

2006 ◽  
Vol 47 (4) ◽  
pp. 477-494 ◽  
Author(s):  
Song-Ping Zhu
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Analytical Formula ◽  
Solution Process ◽  
Closed Form Solution ◽  
Approximate Solutions ◽  
Convertible Bonds ◽  
Form Solution ◽  
Dividend Yield ◽  
Closed Form Analytical Solution

AbstractIn this paper, a closed-form analytical solution for pricing convertible bonds on a single underlying asset with constant dividend yield is presented. A closed-form analytical formula has apparently never been found for American-style convertible bonds (CBs) of finite maturity time although there have been quite a few approximate solutions and numerical approaches proposed. The solution presented here is written in the form of a Taylor's series expansion, which contains infinitely many terms, and thus is completely analytical and in a closed form. Although it is only for the simplest CBs without call or put features, it is nevertheless the first closed-form solution that can be utilised to discuss convertibility analytically. The solution is based on the homotopy analysis method, with which the optimal converting price has been elegantly and temporarily removed in the solution process of each order, and consequently, the solution of a linear problem can be analytically worked out at each order, resulting in a completely analytical solution for the optimal converting price and the CBs' price.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

scholarly journals On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions

2021 ◽  
pp. 25-47
Author(s):  
S. O. Ajibola ◽  
E. O. Oghre ◽  
A. G. Ariwayo ◽  
P. O. Olatunji
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Fractional Differential Equations ◽  
Closed Form Solution ◽  
Boussinesq Equations ◽  
Approximate Solutions ◽  
Form Solution ◽  
Restrictive Assumption ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

By fractional generalised Boussinesq equations we mean equations of the form \begin{equation} \Delta\equiv D_{t}^{2\alpha}-[\mathcal{N}(u)]_{xx}-u_{xxxx}=0, \: 0<\alpha\le1,\label{main}\nonumber \end{equation} where $\mathcal{N}(u)$ is a differentiable function and $\mathcal{N}_{uu}\ne0$ (to ensure nonlinearity). In this paper we lay emphasis on the cubic Boussinesq and Boussinesq-like equations of fractional order and we apply the Laplace homotopy analysis method (LHAM) for their rational and solitary wave solutions respectively. It is true that nonlinear fractional differential equations are often difficult to solve for their {\em exact} solutions and this single reason has prompted researchers over the years to come up with different methods and approach for their {\em analytic approximate} solutions. Most of these methods require huge computations which are sometimes complicated and a very good knowledge of computer aided softwares (CAS) are usually needed. To bridge this gap, we propose a method that requires no linearization, perturbation or any particularly restrictive assumption that can be easily used to solve strongly nonlinear fractional differential equations by hand and simple computer computations with a very quick run time. For the closed form solution, we set $\alpha =1$ for each of the solutions and our results coincides with those of others in the literature.

scholarly journals Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 331 ◽  
Author(s):  
Huda Bakodah ◽  
Abdelhalim Ebaid
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Closed Form Solution ◽  
Approximate Solutions ◽  
Form Solution ◽  
Proportional Delay ◽  
Delay Term ◽  
The Laplace Transform ◽  
Linear Differential ◽  
Delay Differential

The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to establish a closed-form solution. The present closed-form solution is reported for the first time for the Ambartsumian equation. Numerically, the calculations have demonstrated a rapid rate of convergence of the obtained approximate solutions, which are displayed in several graphs. It has also been shown that only a few terms of the new approximate solution were sufficient to achieve extremely accurate numerical results. Furthermore, comparisons of the present results with the existing methods in the literature were introduced.

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

Formulation of surface temperature for laser evaporative pulse heating: The time exponentially decaying pulse case

2002 ◽  
Vol 216 (3) ◽  
pp. 289-299 ◽  
Author(s):  
B S Yilbas ◽  
M Kalyon
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Solid Substrate ◽  
Form Solution ◽  
Solution Temperature ◽  
Heating Process ◽  
Pulse Parameter ◽  
Pulse Profile ◽  
Transform Method

Modelling of the laser heating process is fruitful, since it enhances the understanding of the physical processes involved and minimizes the experimental cost. In the present study, an analytical solution for the temperature distribution inside the solid substrate is obtained using a Laplace transform method. A time exponentially decaying laser pulse profile is introduced in the analysis. The phase change process and recession velocity are accommodated to account for the evaporation at the surface. The closed-form solution obtained is compared with the analytical solution obtained previously for a conduction limited heating case. It is found that the closed-form solution obtained from the present study reduces to a previously obtained analytical solution when the pulse parameter, β∗, is set to zero in the closed-form solution. Temperature predictions from simulations agree well with the results obtained from the closed-form solution.

An analytical solution for jointed tunnel linings in elastic soil or rock

2008 ◽  
Vol 45 (11) ◽  
pp. 1572-1593 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Segmental Lining ◽  
Sophisticated Method ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for tunnel linings that can be idealized as an inner jointed segmental lining and an outer thick-walled cylinder embedded in a homogeneous infinite elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground and lining–lining interfaces. In addition, the closed-form solution is verified by comparing it with finite element results where it is shown to agree well with this more sophisticated method of analysis.

Pipeline Walking due to Temperature Transient: Enhanced Analytical Calculations

2020 ◽  
Author(s):  
Daniel Carneiro ◽  
Renata Carvalhal
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Transient Temperature ◽  
Temperature Profiles ◽  
Linear Temperature ◽  
Temperature Front ◽  
Non Linear ◽  
Closed Form Analytical Solution ◽  
Remarkable Agreement

Abstract Pipeline walking induced by transient temperature profiles as the pipeline heats up is assessed. Firstly, an integrated, closed-form solution is given for a problem for which only an ‘incremental’ solution was available [1]. This involves a short pipeline unrestrained at both ends subject to a linearly ramping temperature front. Secondly, the range of validity of this solution is significantly extended, whilst still presenting it in closed-form. Results are compared with previously published FEA results, presenting remarkable agreement. The closed-form analytical solution is then compared with FEA of more realistic transients (non-linear temperature front). Results show that the linear simplification can introduce excessive conservatism. The FEA results are then examined, and the reason for the excessive conservatism is found to be associated to early expansion of the cold end, which is not observed with the simplified linear front. A simplified incremental solution for non-linear transients is proposed. This is shown to be simple and effective in improving prediction for the range over which where the closed form solution is most conservative.

scholarly journals INFLUENCE OF BEACH LENGTH ON THE DEVELOPMENT OF ESTUARINE DELTAS

2018 ◽  
pp. 12
Author(s):  
Duy Dinh Van ◽  
Hitoshi Tanaka ◽  
Magnus Larson ◽  
Yuta Mitobe ◽  
Viet Nguyen Trung
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
River Mouth ◽  
Form Solution ◽  
River Delta ◽  
Sediment Supply ◽  
Infinite Extent

Larson et al. (1987) proposed a closed-form solution to describe the development of river delta coastlines owing to sediment supply from the river. This solution is for a beach of infinite extent adjacent to the river mouth. However, in reality, the beach length is always finite due to the existence of man-made structures or headlands. It is, therefore, useful to derive a new analytical solution to gain a better understanding of beach behavior under the effect of boundaries.

scholarly journals Closed-Form Solution Procedure for Simulating Debonding in FRP Strips Glued to a Generic Substrate Material

Fibers ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 22
Author(s):  
Enzo Martinelli
Keyword(s):  
Closed Form ◽  
Full Range ◽  
Solution Process ◽  
Closed Form Solution ◽  
Solution Procedure ◽  
Substrate Material ◽  
Form Solution ◽  
Numerical Code ◽  
Mathematical Expressions ◽  
Frp Strips

The present paper proposes a useful closed-form solution for a wide class of mechanical problems, among which one of the most relevant and debated is the deboning process of Fiber-Reinforced Polymer (FRP) strips glued to generic materials and possibly intended as a mode-II fracture process. Specifically, after outlining well-known equations, a novel piecewise analytical formulation based on a cascading solution process is proposed with the aim of keeping the mathematical expressions of the relevant mechanical quantities as simple as possible. Although other analytical solutions and numerical procedures are already available in the literature, the present one is capable of handling the softening or snap-back response deriving from the full-range simulation of the depending process with no need for complex numerical techniques. This is obtained by considering the slip at the free end of the strip as the main displacement control parameter. After some comparisons between the proposed closed-form solution and experimental results available in the literature, some mechanical considerations are highlighted by elaborating on the results of a parametric study considering the variation of the main geometric and mechanical quantities. The numerical code implemented as part of the present study is available to readers in Open Access.

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