justin chirima | Great Zimbabwe University (original) (raw)

Papers by justin chirima

Research paper thumbnail of Pricing a Guaranteed Minimum Maturity Benefit in Uncertain Markets

International Journal of Mathematics in Operational Research, Dec 31, 2022

Research paper thumbnail of Extreme value modelling using the peaks over threshold method, an inverse cumulative uniform distribution approach

International Journal of Hydrology Science and Technology

Research paper thumbnail of An Analysis of the Dynamics of COVID-19 Pandemic in Zimbabwe Using the Extended SEIR Model with Treatment and Quarantine

Research paper thumbnail of Valuation of Corporate Debt and Equity in Uncertain Markets

International Journal of Economics and Financial Issues

In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertaint... more In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertainty, and fuzziness are three basic types of indeterminacy. A multiplicity of differential equations have been designed to depict various processes powered by different kinds of indeterminacy. Among others, these differential equations include uncertain differential equations, stochastic differential equations, and fuzzy differential equations. In this study, we propose that the value of a firm can be described by an uncertain differential equation powered by a geometric canonical Liu process. Uncertain differential equations describe processes driven by uncertainty. Implementing the uncertain Liu option pricing theory, we develop and analyse a framework for valuing debt and equity for a levered firm in uncertain markets. Numerical calculations are demonstrated.

Research paper thumbnail of Uncertain Stochastic Option Pricing in the Presence of Uncertain Jumps

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2019

In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty... more In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty, is introduced and applied to describe the dynamics of a stock price process. This novel class of differential equations is called uncertain stochastic differential equations(USDES) with uncertain jumps. The existence and uniqueness theorem for this class of differential equations is proposed and proved. An appropriate version of the chain rule is derived and applied to solve some examples of USDES with uncertain jumps. The differential equation discussed is applied in an American call option pricing problem. In this problem, it is assumed that the evolution of the stock price is driven by a Brownian motion, the Liu canonical process and an uncertain renewal process. MATLAB is employed for implementing the derived option pricing model. Results show that option prices from the proposed call option pricing formula increase as the jump size increases. As compared to the proposed call optio...

Research paper thumbnail of Application of statistical control charts to climate change detection in Masvingo city, Zimbabwe

This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Ave... more This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charting techniques to determine if the climate of Masvingo station in Zimbabwe has changed over the past years. In particular, the climate indicator considered in this work is the annual air temperatures for Masvingo station for the period 1952 to 2001. The two control charts were then applied to the data and both techniques proved effective in detecting climate change. However, the CUSUM chart detected a significant shift in mean annual air temperatures in 1983 while the EWMA chart detected the shift in 1993. The two methods suggested that the origin of the shift was in 1981. An upward shift in the mean level and a subsequent test in the mean difference points to the fact that the mean annual temperature is going up. This means that the temperatures are getting warmer by the years. The use of these two techniques confirms the existence of climate change in Masvingo ...

Research paper thumbnail of Application of statistical control charts to climate change detection in Masvingo city, Zimbabwe

This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Ave... more This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charting techniques to determine if the climate of Masvingo station in Zimbabwe has changed over the past years. In particular, the climate indicator considered in this work is the annual air temperatures for Masvingo station for the period 1952 to 2001. The two control charts were then applied to the data and both techniques proved effective in detecting climate change. However, the CUSUM chart detected a significant shift in mean annual air temperatures in 1983 while the EWMA chart detected the shift in 1993. The two methods suggested that the origin of the shift was in 1981. An upward shift in the mean level and a subsequent test in the mean difference points to the fact that the mean annual temperature is going up. This means that the temperatures are getting warmer by the years. The use of these two techniques confirms the existence of climate change in Masvingo ...

Research paper thumbnail of Application of statistical control charts to climate change detection in Masvingo city, Zimbabwe

This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Ave... more This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charting techniques to determine if the climate of Masvingo station in Zimbabwe has changed over the past years. In particular, the climate indicator considered in this work is the annual air temperatures for Masvingo station for the period 1952 to 2001. The two control charts were then applied to the data and both techniques proved effective in detecting climate change. However, the CUSUM chart detected a significant shift in mean annual air temperatures in 1983 while the EWMA chart detected the shift in 1993. The two methods suggested that the origin of the shift was in 1981. An upward shift in the mean level and a subsequent test in the mean difference points to the fact that the mean annual temperature is going up. This means that the temperatures are getting warmer by the years. The use of these two techniques confirms the existence of climate change in Masvingo ...

Research paper thumbnail of Option Pricing Model for Stocks in Uncertain Stochastic Markets

This paper examines an option pricing model for stocks in uncertain stochastic markets. Randomnes... more This paper examines an option pricing model for stocks in uncertain stochastic markets. Randomness has been widely accepted in modelling indeterminacy in situations where substantial sample data is available. Recently, uncertainty theory has been used by Liu to describe indeterminacy in situations where sample data is not sufficiently available to warrant the use of probability theory. In this paper, a stock model where stock prices are driven by both uncertainty and randomness is presented and examined. Stock prices are assumed to be driven by an uncertain stochastic process. There exist some interactions between a Weiner process and a Liu process, thus an uncertain stochastic process is hybrid in nature. An option pricing model is derived for uncertain stochastic markets and an example is given to illustrate the application of the model. The derived pricing formula produces improved results because it caters for both forms of indeterminacy, that is randomness and uncertainty.

Research paper thumbnail of Numerical methods for first order uncertain stochastic differential equations

International Journal of Mathematics in Operational Research

Research paper thumbnail of Pricing a Guaranteed Minimum Maturity Benefit in Uncertain Markets

International Journal of Mathematics in Operational Research, Dec 31, 2022

Research paper thumbnail of Extreme value modelling using the peaks over threshold method, an inverse cumulative uniform distribution approach

International Journal of Hydrology Science and Technology

Research paper thumbnail of An Analysis of the Dynamics of COVID-19 Pandemic in Zimbabwe Using the Extended SEIR Model with Treatment and Quarantine

Research paper thumbnail of Valuation of Corporate Debt and Equity in Uncertain Markets

International Journal of Economics and Financial Issues

In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertaint... more In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertainty, and fuzziness are three basic types of indeterminacy. A multiplicity of differential equations have been designed to depict various processes powered by different kinds of indeterminacy. Among others, these differential equations include uncertain differential equations, stochastic differential equations, and fuzzy differential equations. In this study, we propose that the value of a firm can be described by an uncertain differential equation powered by a geometric canonical Liu process. Uncertain differential equations describe processes driven by uncertainty. Implementing the uncertain Liu option pricing theory, we develop and analyse a framework for valuing debt and equity for a levered firm in uncertain markets. Numerical calculations are demonstrated.

Research paper thumbnail of Uncertain Stochastic Option Pricing in the Presence of Uncertain Jumps

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2019

In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty... more In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty, is introduced and applied to describe the dynamics of a stock price process. This novel class of differential equations is called uncertain stochastic differential equations(USDES) with uncertain jumps. The existence and uniqueness theorem for this class of differential equations is proposed and proved. An appropriate version of the chain rule is derived and applied to solve some examples of USDES with uncertain jumps. The differential equation discussed is applied in an American call option pricing problem. In this problem, it is assumed that the evolution of the stock price is driven by a Brownian motion, the Liu canonical process and an uncertain renewal process. MATLAB is employed for implementing the derived option pricing model. Results show that option prices from the proposed call option pricing formula increase as the jump size increases. As compared to the proposed call optio...

Research paper thumbnail of Application of statistical control charts to climate change detection in Masvingo city, Zimbabwe

This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Ave... more This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charting techniques to determine if the climate of Masvingo station in Zimbabwe has changed over the past years. In particular, the climate indicator considered in this work is the annual air temperatures for Masvingo station for the period 1952 to 2001. The two control charts were then applied to the data and both techniques proved effective in detecting climate change. However, the CUSUM chart detected a significant shift in mean annual air temperatures in 1983 while the EWMA chart detected the shift in 1993. The two methods suggested that the origin of the shift was in 1981. An upward shift in the mean level and a subsequent test in the mean difference points to the fact that the mean annual temperature is going up. This means that the temperatures are getting warmer by the years. The use of these two techniques confirms the existence of climate change in Masvingo ...

Research paper thumbnail of Application of statistical control charts to climate change detection in Masvingo city, Zimbabwe

This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Ave... more This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charting techniques to determine if the climate of Masvingo station in Zimbabwe has changed over the past years. In particular, the climate indicator considered in this work is the annual air temperatures for Masvingo station for the period 1952 to 2001. The two control charts were then applied to the data and both techniques proved effective in detecting climate change. However, the CUSUM chart detected a significant shift in mean annual air temperatures in 1983 while the EWMA chart detected the shift in 1993. The two methods suggested that the origin of the shift was in 1981. An upward shift in the mean level and a subsequent test in the mean difference points to the fact that the mean annual temperature is going up. This means that the temperatures are getting warmer by the years. The use of these two techniques confirms the existence of climate change in Masvingo ...

Research paper thumbnail of Application of statistical control charts to climate change detection in Masvingo city, Zimbabwe

This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Ave... more This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charting techniques to determine if the climate of Masvingo station in Zimbabwe has changed over the past years. In particular, the climate indicator considered in this work is the annual air temperatures for Masvingo station for the period 1952 to 2001. The two control charts were then applied to the data and both techniques proved effective in detecting climate change. However, the CUSUM chart detected a significant shift in mean annual air temperatures in 1983 while the EWMA chart detected the shift in 1993. The two methods suggested that the origin of the shift was in 1981. An upward shift in the mean level and a subsequent test in the mean difference points to the fact that the mean annual temperature is going up. This means that the temperatures are getting warmer by the years. The use of these two techniques confirms the existence of climate change in Masvingo ...

Research paper thumbnail of Option Pricing Model for Stocks in Uncertain Stochastic Markets

This paper examines an option pricing model for stocks in uncertain stochastic markets. Randomnes... more This paper examines an option pricing model for stocks in uncertain stochastic markets. Randomness has been widely accepted in modelling indeterminacy in situations where substantial sample data is available. Recently, uncertainty theory has been used by Liu to describe indeterminacy in situations where sample data is not sufficiently available to warrant the use of probability theory. In this paper, a stock model where stock prices are driven by both uncertainty and randomness is presented and examined. Stock prices are assumed to be driven by an uncertain stochastic process. There exist some interactions between a Weiner process and a Liu process, thus an uncertain stochastic process is hybrid in nature. An option pricing model is derived for uncertain stochastic markets and an example is given to illustrate the application of the model. The derived pricing formula produces improved results because it caters for both forms of indeterminacy, that is randomness and uncertainty.

Research paper thumbnail of Numerical methods for first order uncertain stochastic differential equations

International Journal of Mathematics in Operational Research