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This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part.

Hedging and Malliavin calculus techniques recently developed under a stochastic string framework are applied.

A necessary and sufficient condition for the hedging portfolio to have no bank account part is found. This condition is applied to a barrier option, and an example of a contingent claim whose hedging portfolio has a bank account part different from zero is provided.

To the best of the authors’ knowledge, this is the first time that this issue has been addressed in the literature.

The purpose of this paper is to study the problem of optimal Ramsey taxation in a finite-planning-horizon, representative-agent endogenous growth model including government expenditures as a productive input in capital formation and also with hidden actions.

Technically, Malliavin calculus and forward integrals are naturally introduced into the macroeconomic theory when economic agents are faced with different information structures arising from a non-Markovian environment.

The major result shows that the well-known Judd-Chamley Theorem holds almost surely if the depreciation rate is strictly positive, otherwise Judd-Chamley Theorem only holds for a knife-edge case or on a Lebesgue measure-zero set when the physical capital is completely sustainable.

The author believes that the approach developed as well as the major result established is new and relevant.

Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper candidate for modelling this empirical phenomena. IBm. however. is not a semimartingale process. For this reason. it is very hard to apply such processes for asset price modelling.

Without using Ito formula, we investigate the IBm interest rate theory‘ We obtain a pure discount bond price. and Greeks by using Malllavin calculus.

The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.

The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.

In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.

In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. The purpose of this paper is to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time.

The authors consider a market suffering from a financial crisis. The authors provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. Furthermore, the underlying price sensitivities are derived.

The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during a financial crisis more precise. A numerical application is provided for determining the premium for a call and a put European option along with the underlying price sensitivities for each option.

An alternative option pricing model is introduced that performs better than existing ones, especially during a financial crisis.

The purpose of this paper is to review the life of the famous mathematician Kiyosi Itô and discuss his influence on the study of agricultural finance and agricultural economics.

This paper is a qualitative historical review.

The paper provides a biographical stretch of Itô's life. It is shown that his influence started to infiltrate the agricultural economics profession at around 1985 and is currently a major influence of a range of economic issues from farm policy to agricultural investments.

The biography is limited to a review of Itô's academic life and influence.

The paper offers a historical perspective on how probability emerged as a critical piece of the economic puzzle. For scholars and practitioners of agricultural finance, the paper provides an in depth review of how Itô processes have, and can, be used.

This paper provides a historical perspective on Itô that is of use to students and scholars of rural credit. This is the first “biography” of Itô to discuss his influence on agricultural finance and agricultural economics.

This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation.

This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap.

The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap.

The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model.

This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.

The paper aims to compare and clarify the differences and between the two well-known decomposition spectral techniques; the Winer–Chaos expansion (WCE) and the Winer–Hermite expansion (WHE). The details of the two decompositions are outlined. The difficulties arise when using the two techniques are also mentioned along with the convergence orders. The reader can also find a collection of references to understand the two decompositions with their origins. The geometrical Brownian motion is considered as an example for an important process with exact solution for the sake of comparison. The two decompositions are found practical in analysing the SDEs. The WCE is, in general, simpler, while WHE is more efficient as it is the limit of WCE when using infinite number of random variables. The Burgers turbulence is considered as a nonlinear example and WHE is shown to be more efficient in detecting the turbulence. In general, WHE is more efficient especially in case of nonlinear and/or non-Gaussian processes.

The paper outlined the technical and literature review of the WCE and WHE techniques. Linear and nonlinear processes are compared to outline the comparison along with the convergence of both techniques.

The paper shows that both decompositions are practical in solving the stochastic differential equations. The WCE is found simpler and WHE is the limit when using infinite number of random variables in WCE. The WHE is more efficient especially in case of nonlinear problems.

Applicable for SDEs with square integrable processes and coefficients satisfying Lipschitz conditions.

This paper fulfils a comparison required by the researchers in the stochastic analysis area. It also introduces a simple efficient technique to model the flow turbulence in the physical domain.

This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models.

The paper uses theory of forecasting to find criteria of predictability of market parameters such as volatilities and the appreciation rates.

It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into an incomplete one. The paper shows that market incompleteness is also non-robust: for any incomplete market from a wide class of models, there exists a complete market model with arbitrarily close paths of the stock prices and the market parameters.

The paper results lead to a counterintuitive conclusion that the incomplete markets are indistinguishable in the terms of the market statistics.