Corina Averbuj | CONICET, UBA, UNSAM (original) (raw)

Papers by Corina Averbuj

Research paper thumbnail of Stationary solutions for two nonlinear Black–Scholes type equations

Applied Numerical Mathematics, 2003

ABSTRACT

Research paper thumbnail of Stationary solutions for two nonlinear Black–Scholes type equations

Applied Numerical Mathematics, 2003

ABSTRACT

Research paper thumbnail of A Black–Scholes option pricing model with transaction costs

Journal of Mathematical Analysis and Applications, 2005

Research paper thumbnail of Crecimiento Endógeno

Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnol... more Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of Nonlinear-differential evolution equation arising in option pricing when including transaction costs : a viscosity solution approach 1

Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an i... more Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an increasing interest in problems arising in Financial Mathematics and in particular in derivatives pricing. The standard approach to this problem leads to the study of parabolic equations.One of the classic assumptions of the BlackScholes model solution (1973) is that the investor’s portfolio revalues continuously. This dynamic implies transaction costs, due to the buying/selling of stocks for maintaining the portfolio’s equilibrium. BlackScholes models that include proportional transaction costs have been studied by many authors Leland (1985).In this work we suppose that transaction costs behave as a non-increasing positive linear function, h(x) =a-bx, (a, b>0) which depends on the stock trading needed for hedging the portfolio that replicates the contingent claim.Moreover, if the underlying asset follows a jump-diffusion process, Merton (1993), we obtain an integro-differential evolut...

Research paper thumbnail of A Jump Option pricing model with Transaction costs

Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an inc... more Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an increasing interest on problems arising in Financial Mathematics and in particular on derivatives pricing.The standard approach to this problem leads to the study of equations of parabolic type.

Research paper thumbnail of Crecimiento Endógeno

Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnol... more Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of Crecimiento Endógeno

Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnol... more Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of A Jump Option pricing model with Transaction costs

Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an inc... more Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an increasing interest on problems arising in Financial Mathematics and in particular on derivatives pricing.The standard approach to this problem leads to the study of equations of parabolic type.

Research paper thumbnail of Nonlinear-differential evolution equation arising in option pricing when including transaction costs : a viscosity solution approach 1

Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an i... more Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an increasing interest in problems arising in Financial Mathematics and in particular in derivatives pricing. The standard approach to this problem leads to the study of parabolic equations.One of the classic assumptions of the BlackScholes model solution (1973) is that the investor’s portfolio revalues continuously. This dynamic implies transaction costs, due to the buying/selling of stocks for maintaining the portfolio’s equilibrium. BlackScholes models that include proportional transaction costs have been studied by many authors Leland (1985).In this work we suppose that transaction costs behave as a non-increasing positive linear function, h(x) =a-bx, (a, b>0) which depends on the stock trading needed for hedging the portfolio that replicates the contingent claim.Moreover, if the underlying asset follows a jump-diffusion process, Merton (1993), we obtain an integro-differential evolut...

Research paper thumbnail of Nonlinear Integral-Differential evolution equation arising in option pricing when including transaction costs: A viscosity solution approach

Since Black and Scholes´s paper (1973) presents a formula to pricing option, there has been an in... more Since Black and Scholes´s paper (1973) presents a formula to pricing option, there has been an increasing interest on problems arising in Financial Mathematics and in particular on derivatives pricing. The standard approach to this problem leads to the study of equations of parabolic type. One of the classic assumptions with the Black- Scholes models resolution (1973) is that the investor's portfolio revalue in a continuous form. This dynamic implies transaction costs, due to the buy/sell of necessary stocks to maintain the portfolio's equilibrium. Black- Scholes models which include proportional transaction costs were studied by many authors (Leland, 1985). In this work we suppose that transaction costs behave as a no increasing lineal function, h(x) =a-bx, (a, b>0), depending on the trading stocks need to hedge the portfolio that replicates the contingent claim. Moreover, if the underlying asset follows a jump-diffusion process, (Merton, 1993), we obtain an Evolution In...

Research paper thumbnail of Rezagos de inversión y crecimiento limitado de la población en unmodelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of A Generalized Solow Nonautonomous Model with Delay and Bounded Population Growth

In this paper we consider a nonautonomous functional differential equation obtained when the clas... more In this paper we consider a nonautonomous functional differential equation obtained when the classical Solow model extends by adding a delay in the new capital installed and the active population is not decreasing and asymptotically bounded. The existence of an unique solution is proved and suffcient conditions are given for both stability and boundedness. The evolution of this equation over time and its convergence, or not, to teady states is exemplified through numerical simulations.

Research paper thumbnail of Solutions to a stationary nonlinear Black–Scholes type equation

Journal of Mathematical Analysis and Applications, 2002

We study by topological methods a nonlinear differential equation generalizing the Black–Scholes ... more We study by topological methods a nonlinear differential equation generalizing the Black–Scholes formula for an option pricing model with stochastic volatility. We prove the existence of at least a solution of the stationary Dirichlet problem applying an upper and lower solutions method. Moreover, we construct a solution by an iterative procedure.

Research paper thumbnail of Stationary solutions for two nonlinear Black–Scholes type equations

Applied Numerical Mathematics, 2003

ABSTRACT

Research paper thumbnail of Stationary solutions for two nonlinear Black–Scholes type equations

Applied Numerical Mathematics, 2003

ABSTRACT

Research paper thumbnail of A Black–Scholes option pricing model with transaction costs

Journal of Mathematical Analysis and Applications, 2005

Research paper thumbnail of Crecimiento Endógeno

Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnol... more Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of Nonlinear-differential evolution equation arising in option pricing when including transaction costs : a viscosity solution approach 1

Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an i... more Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an increasing interest in problems arising in Financial Mathematics and in particular in derivatives pricing. The standard approach to this problem leads to the study of parabolic equations.One of the classic assumptions of the BlackScholes model solution (1973) is that the investor’s portfolio revalues continuously. This dynamic implies transaction costs, due to the buying/selling of stocks for maintaining the portfolio’s equilibrium. BlackScholes models that include proportional transaction costs have been studied by many authors Leland (1985).In this work we suppose that transaction costs behave as a non-increasing positive linear function, h(x) =a-bx, (a, b>0) which depends on the stock trading needed for hedging the portfolio that replicates the contingent claim.Moreover, if the underlying asset follows a jump-diffusion process, Merton (1993), we obtain an integro-differential evolut...

Research paper thumbnail of A Jump Option pricing model with Transaction costs

Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an inc... more Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an increasing interest on problems arising in Financial Mathematics and in particular on derivatives pricing.The standard approach to this problem leads to the study of equations of parabolic type.

Research paper thumbnail of Crecimiento Endógeno

Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnol... more Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of Crecimiento Endógeno

Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnol... more Rezagos de inversión y crecimiento limitado de la población en un modelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of A Jump Option pricing model with Transaction costs

Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an inc... more Since Black and Scholes´s paper ([2]) presents a formula to pricing option, there has been an increasing interest on problems arising in Financial Mathematics and in particular on derivatives pricing.The standard approach to this problem leads to the study of equations of parabolic type.

Research paper thumbnail of Nonlinear-differential evolution equation arising in option pricing when including transaction costs : a viscosity solution approach 1

Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an i... more Since the Black-Scholes paper (1973) presented a formula for pricing options, there has been an increasing interest in problems arising in Financial Mathematics and in particular in derivatives pricing. The standard approach to this problem leads to the study of parabolic equations.One of the classic assumptions of the BlackScholes model solution (1973) is that the investor’s portfolio revalues continuously. This dynamic implies transaction costs, due to the buying/selling of stocks for maintaining the portfolio’s equilibrium. BlackScholes models that include proportional transaction costs have been studied by many authors Leland (1985).In this work we suppose that transaction costs behave as a non-increasing positive linear function, h(x) =a-bx, (a, b>0) which depends on the stock trading needed for hedging the portfolio that replicates the contingent claim.Moreover, if the underlying asset follows a jump-diffusion process, Merton (1993), we obtain an integro-differential evolut...

Research paper thumbnail of Nonlinear Integral-Differential evolution equation arising in option pricing when including transaction costs: A viscosity solution approach

Since Black and Scholes´s paper (1973) presents a formula to pricing option, there has been an in... more Since Black and Scholes´s paper (1973) presents a formula to pricing option, there has been an increasing interest on problems arising in Financial Mathematics and in particular on derivatives pricing. The standard approach to this problem leads to the study of equations of parabolic type. One of the classic assumptions with the Black- Scholes models resolution (1973) is that the investor's portfolio revalue in a continuous form. This dynamic implies transaction costs, due to the buy/sell of necessary stocks to maintain the portfolio's equilibrium. Black- Scholes models which include proportional transaction costs were studied by many authors (Leland, 1985). In this work we suppose that transaction costs behave as a no increasing lineal function, h(x) =a-bx, (a, b>0), depending on the trading stocks need to hedge the portfolio that replicates the contingent claim. Moreover, if the underlying asset follows a jump-diffusion process, (Merton, 1993), we obtain an Evolution In...

Research paper thumbnail of Rezagos de inversión y crecimiento limitado de la población en unmodelo de Solow-Swan con tecnologías de crecimiento endógeno

Research paper thumbnail of A Generalized Solow Nonautonomous Model with Delay and Bounded Population Growth

In this paper we consider a nonautonomous functional differential equation obtained when the clas... more In this paper we consider a nonautonomous functional differential equation obtained when the classical Solow model extends by adding a delay in the new capital installed and the active population is not decreasing and asymptotically bounded. The existence of an unique solution is proved and suffcient conditions are given for both stability and boundedness. The evolution of this equation over time and its convergence, or not, to teady states is exemplified through numerical simulations.

Research paper thumbnail of Solutions to a stationary nonlinear Black–Scholes type equation

Journal of Mathematical Analysis and Applications, 2002

We study by topological methods a nonlinear differential equation generalizing the Black–Scholes ... more We study by topological methods a nonlinear differential equation generalizing the Black–Scholes formula for an option pricing model with stochastic volatility. We prove the existence of at least a solution of the stationary Dirichlet problem applying an upper and lower solutions method. Moreover, we construct a solution by an iterative procedure.