本文選題：可轉(zhuǎn)換債券 + 變分不等式　； 參考：《蘇州大學(xué)》2012年碩士論文

【摘要】：本文研究下述變分不等式的邊值問(wèn)題：其中 問(wèn)題(1)-(2)與一個(gè)永久可轉(zhuǎn)換債券的定價(jià)問(wèn)題有關(guān)。χ表示公司的總資產(chǎn),f(χ)表示公司可轉(zhuǎn)換債券的總價(jià)值,χ-f(χ)是公司股票的價(jià)格。δ為股票的分紅率,σ為公司總資產(chǎn)的波動(dòng)率,r為無(wú)風(fēng)險(xiǎn)利率,rδ。c是債券的分紅率,γ是可轉(zhuǎn)債全部轉(zhuǎn)換為股票后在公司總資產(chǎn)中所占的比率,0γ1,α是公司總資產(chǎn)的上限。(參見(jiàn)[1]) 問(wèn)題(1)-(2)雖然是一維問(wèn)題,但因?yàn)樗阕覰是二階非線性的且在χ=0是退化的,該問(wèn)題沒(méi)有顯示解,且理論研究具有相當(dāng)?shù)碾y度。文[1]的作者運(yùn)用隨機(jī)分析的方法,證明了問(wèn)題(1)-(2)解的存在性,但他們未能證明解的唯一性,對(duì)自由邊界的位置也沒(méi)能作出估計(jì)。 本文利用自由邊界問(wèn)題理論中的懲罰方法,通過(guò)適當(dāng)?shù)谋平撟C和精細(xì)的估計(jì),證明了問(wèn)題(1)-(2)在C([0,α])∩W2,∞((η,α))(η為(0,α)中任一數(shù))中解的存在性和唯一性,并且得到了自由邊界點(diǎn)的上下界估計(jì)。本文所用的方法,還可以推廣來(lái)研究相應(yīng)的具有有限到期時(shí)間的(與時(shí)間有關(guān)的)可轉(zhuǎn)換債券的定價(jià)問(wèn)題。
[Abstract]:In this paper, we study the boundary value problems of the following variational inequalities: The problem is related to the pricing of a permanent convertible bond. 蠂 denotes the total assets of the company f (蠂) denotes the total value of the convertible bond, 蠂-f (蠂) is the price of the company's stock, 未 is the dividend ratio of the stock, 蟽 is the fluctuation of the total assets of the company R is the risk-free interest rate, r 未. C is the dividend ratio of bonds, 緯 is the ratio of convertible bonds to stocks, and a is the upper limit of the total assets of the company. (see [1]) Although the problem is one-dimensional, the operator N is second-order nonlinear and degenerate at 蠂 ~ 0. The problem does not show a solution, and the theoretical study is quite difficult. The authors of paper [1] proved the existence of the solution of the problem by means of stochastic analysis, but they failed to prove the uniqueness of the solution and to estimate the position of the free boundary. In this paper, by using the penalty method in the theory of free boundary problems, we prove the existence and uniqueness of the solution of the problem (1) in C ([0, 偽]) 螕 W 2, 鈭，

本文編號(hào)：1833939