Stochastic Predetermination of Risk and Hedging Skills for Small Scale Entrepreneurs

Main Article Content

I. O. Longe
E. O. Ayoola


Faced with the issue of hedging risk, small businesses entrepreneurs are investing considerable resources in risk management systems in as much as to maximize profit and stay operational, as such, the types of risk are identified and quantified within each business. This paper focused on the application of stochastic processes to prove that risk could be predetermined and hence determine which kind of small business should be insured to mitigate money spent on insurance.

Hedging, risk, stochastic processes, entrepreneurship.

Article Details

How to Cite
Longe, I. O., & Ayoola, E. O. (2019). Stochastic Predetermination of Risk and Hedging Skills for Small Scale Entrepreneurs. Journal of Advances in Mathematics and Computer Science, 33(6), 1-13.
Original Research Article


Avellaneda MA, Levy, Paras A. Pricing and Hedging derivative securities in markets with uncertain volatilities. Applied Mathematical France. 1995;2:73-88.

Ekhaguere GOS. Class note book on stochastic analysis and financial markets. Unpublished; 2010.

Filipovi´ CD. Interest rate models. Lecture Notes, LMU University of M¨ınchen. 2006;79-96.

Follmer H, Schweizer M. Hedging of contingent claims under incomplete information. In: Eliot RJ, Davis MHA, Editors, Applied Stochastic Analysis. 1991;389-414.

Grandell J. Doubly stochastic Poisson processes. Lecture Note in Mathematics 529, Springer, Berlin; 1996.

Grandell J. Mixed Poisson processes - Chapman and Hall, London; 1997.

Harrison J. Brownian motion and stochastic flow systems. Wiley, New York; 1985.

Jensen B, Nielsen J. Pricing by no-arbitrage in time series models in econometrics, finance and other fields. Ed. by Cox, D., Hinkley, D. and Barndorff-Nielson. Chapman Hall, London; 1996.

Jarroo R. Derivative securities markets, market manipulation and option pricing theory. Journal of Financial and Quantitative Analysis. 1994;29:241-261.

Paul Embrechts, Rudiger Frey, Hansjorg Furrer. Stochastic processes in insurance and finance. ETH Zurich, Switzerland; 1999.

Cox J, Ross S, Rubinstein M. Options pricing: A simplified approach. Journal of Financial Economics. 1979;7:229-263.

Harrison J, Kreps D. Martingale and stochastic integrals in the theory of continuous trading. Stochastic Processes and Applications. 1979;11:215-260.

Gerber H. An introduction to mathematical risk theory. Huebier Foundation Monographs 8, Distributed by Richard D. Irwin Inc. Homewood Illinois; 1979.

Schmidt KD. Lectures on risk theory. Teubner-Verlag, Stuttgart; 1996.

Delaen F, Haezendonck J. A martingale approach to premium calculation principles in an arbitrage - free market. Insurance: Mathematics and Economics. 1989;8:269-277.

Sondermann D. Reinsurance in arbitrage free markets’ insurance. Mathematics and Economics. 1991;10:191-202.

Darryll Hendrick. Evaluation of value-at-risk models using historical date. Economic Policy Review. 1996;2(1).

Kopp P. Martingale and stochastic integrals. Cambridge University Press, Cambridge; 1984.

Michelle M. Harner. Mitigating financial risk for small Business Entrepreneur. Ohio State Entrepreneurial Business Law Journal. 2011;6:469.

Morgan JP. Introduction to risk metrics. Fourth Edition, Morgan Guaranty Trust Company, Risk Management Services. Jacques Longerstaey. 1995;1-212:648-4936.

Bengtsson M, Olsbo V. Value-at-risk using stochastic volatility models. Master’s Thesis, Department of Mathematical Statistics, University of Gothenburg; 2003.

Eberlein E, Kallsen J, Kristen J. Risk management based on stochastic volatility. FDM Preprint 72, University of Freiburg; 2001.


Mingin Xu. Risk measure pricing and hedging in incomplete markets. Finance 0406004, University Library of Munich, Germany; 2005.

Myeni R. The pricing of the American option. The Annals of Applied Probability. 1992;2:1–23.

Nils H. Hakansson. Optimal entrepreneurial decisions in a completely stochastic environment. Management Science, University of California, Berkeley, U.S.A. 1971;17(7).

Panjer H, Willmot G. Insurance risk models. Society of Actuaries, Schaumburg, Illinois; 1992.

Lando D. Modelling bonds and derivatives with credit risk. In Mathematic Financial Derivatives, Ed. by M. Dempster and S. Pliska. Cambridge University press, Cambridge. 1997;369-393.

Frey R, Sommer D. A systematic approach to pricing and hedging of international financial markets. Unpublished; 1996.

Gooverts MF, Vylder DE, Haezendonck J. Insurance premiums. North Holland, Amsterdam; 1984.

Frey R, Sin C. Bounds on European option prices under stochastic volatility. Mathematical Finance. 1999;9:97-116.