We obtain a Black Scholes formula for the arbitrage free pricing of European Call options with constant coefficients when the underlying stock generates dividends. To hedge the Call option, we will always borrow mon...We obtain a Black Scholes formula for the arbitrage free pricing of European Call options with constant coefficients when the underlying stock generates dividends. To hedge the Call option, we will always borrow money form bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation,). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rate r. The corresponding Black Scholes formula is given. We notice that it is in fact the borrowing rate that plays the role in the pricing formula.展开更多
Reform dividends refer to the improvements in certain economic actors under the new, reformed institutional system as compared against the original system. Reform leads to greater economic growth potential by changing...Reform dividends refer to the improvements in certain economic actors under the new, reformed institutional system as compared against the original system. Reform leads to greater economic growth potential by changing the institutional environment, which in turn increases the vibrancy and innovation of economic actors. The most economically convenient system is also in actuality the most effective market economic system. Reform based on public and collective actions should be based on the following principle： if institutional reform is evolving towards the enhancement of economic convenience, then we can be sure that reform is embarking on the path of releasing dividends.展开更多
In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the...In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.展开更多
The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the ab...The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.展开更多
In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rate...In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rates,tax rates,and transaction fees,inevitably impact these strategies.By incorporating appropriate constraints,a multi-type mixed strategy can better simulate real-world transactions.Following the approach of Liu et al.[28],we examine a classical compound Poisson risk model that incorporates the constraints of constant interest rates and a periodic-threshold mixed dividend strategy.In this model,the surplus process of insurance companies is influenced by several factors.These factors include constant interest rates,continuously distributed dividends within intervals(threshold dividend strategy),and dividends at discrete time points(periodic dividend strategy).We derive the piecewise integro-differential equations(IDEs)that describe the expected present value of dividends(EPVDs)until ruin time and the Gerber-Shiu expected discounted penalty function.Furthermore,we provide explicit solutions to these IDEs using an alternative method based on the inverse Laplace transform combined with the Dickson-Hipp operator.This enables us to obtain explicit expressions for the dividend and Gerber-Shiu functions.Additionally,we present examples to illustrate the application of our results.展开更多
In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with...In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.展开更多
This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the...This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.展开更多
This paper deals with options on assets, such as stocks or indexes, which pay cash dividends. Pricing methods which consider discrete dividends are usually computationally expensive and become infeasible when one cons...This paper deals with options on assets, such as stocks or indexes, which pay cash dividends. Pricing methods which consider discrete dividends are usually computationally expensive and become infeasible when one considers multiple dividends paid during the option lifetime. This is the case of long-term options and options on indexes. The first purpose of this paper is to assess efficient and accurate numerical procedures which yield consistent prices for both European and American options when the underlying asset pays discrete dividends. The authors then analyze some methodologies to extract information on implied volatilities and dividends from quoted option prices. Implied dividends can also be computed using a modified version of the well-known put-call parity relationship. This technique is straightforward, nevertheless, its use is limited to European options, and when dealing with equities, most traded options are of American type. As an alternative, the numerical inversion of pricing methods, such as efficient interpolated binomial method, can be used. This paper applies different procedures to obtain implied volatilities and dividends of listed stocks of the Italian derivatives market （IDEM）.展开更多
文摘We obtain a Black Scholes formula for the arbitrage free pricing of European Call options with constant coefficients when the underlying stock generates dividends. To hedge the Call option, we will always borrow money form bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation,). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rate r. The corresponding Black Scholes formula is given. We notice that it is in fact the borrowing rate that plays the role in the pricing formula.
文摘Reform dividends refer to the improvements in certain economic actors under the new, reformed institutional system as compared against the original system. Reform leads to greater economic growth potential by changing the institutional environment, which in turn increases the vibrancy and innovation of economic actors. The most economically convenient system is also in actuality the most effective market economic system. Reform based on public and collective actions should be based on the following principle： if institutional reform is evolving towards the enhancement of economic convenience, then we can be sure that reform is embarking on the path of releasing dividends.
基金supported by the NSFC(11171101)Doctoral Fund of Education Ministry of China(20104306110001)the Graduate Research and Innovation Fund of Hunan Province(CX2011B197)
文摘In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.
基金Supported by the National Natural Science Foundation of China(11701319,11571198).
文摘The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.
基金supported by the National Natural Science Foundation of China(12361095)the Jiangxi Provincial Natural Science Foundation(20232BAB201028)。
文摘In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rates,tax rates,and transaction fees,inevitably impact these strategies.By incorporating appropriate constraints,a multi-type mixed strategy can better simulate real-world transactions.Following the approach of Liu et al.[28],we examine a classical compound Poisson risk model that incorporates the constraints of constant interest rates and a periodic-threshold mixed dividend strategy.In this model,the surplus process of insurance companies is influenced by several factors.These factors include constant interest rates,continuously distributed dividends within intervals(threshold dividend strategy),and dividends at discrete time points(periodic dividend strategy).We derive the piecewise integro-differential equations(IDEs)that describe the expected present value of dividends(EPVDs)until ruin time and the Gerber-Shiu expected discounted penalty function.Furthermore,we provide explicit solutions to these IDEs using an alternative method based on the inverse Laplace transform combined with the Dickson-Hipp operator.This enables us to obtain explicit expressions for the dividend and Gerber-Shiu functions.Additionally,we present examples to illustrate the application of our results.
基金The NSF (11201217) of Chinathe NSF (20132BAB211010) of Jiangxi Province
文摘In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.
文摘This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.
文摘This paper deals with options on assets, such as stocks or indexes, which pay cash dividends. Pricing methods which consider discrete dividends are usually computationally expensive and become infeasible when one considers multiple dividends paid during the option lifetime. This is the case of long-term options and options on indexes. The first purpose of this paper is to assess efficient and accurate numerical procedures which yield consistent prices for both European and American options when the underlying asset pays discrete dividends. The authors then analyze some methodologies to extract information on implied volatilities and dividends from quoted option prices. Implied dividends can also be computed using a modified version of the well-known put-call parity relationship. This technique is straightforward, nevertheless, its use is limited to European options, and when dealing with equities, most traded options are of American type. As an alternative, the numerical inversion of pricing methods, such as efficient interpolated binomial method, can be used. This paper applies different procedures to obtain implied volatilities and dividends of listed stocks of the Italian derivatives market （IDEM）.
