Daniel Dufresne — Publications


Vázquez-Abad, Flynn, T., and Dufresne, D. (2017). Dynamic mollifiers to deal with discontinuities in machine learning. Submitted for publication.

Dufresne, D., and Zhang, Z. (2017). Discounted sums with renewal times. Submitted for publication. 21 pages.

Chateau, J.-P., and Dufresne, D. (2017). Gram-Charlier processes and applications to option pricing. Journal of Probability and Statistics, vol. 2017, Article ID 8690491.

Dufresne, D. (2016). Introduction to Stochastic Calculus. Ebook, in preparation. For actuarial and finance students, at undergraduate or Master's level, with solved exercises. Draft of Chapter 1   Exercises 1.

Dufresne, D., and Pitman, J. (2016). Properties of beta and gamma variables. In preparation.

Dufresne, D., and Vázquez-Abad, F. (2016). Downsizing, upsizing for Asian options. In preparation.

Dufresne, D., and Li, H. (2016). Pricing Asian options: Convergence of Gram-Charlier series. Actuarial Research Clearing House 2016.2. Also here.

Dufresne, D., Vázquez-Abad, F.J., and Chin, S. (2014). Change of measure for the square root process. Proceedings of the 2014 Winter Simulation Conference. A. Tolk, S. D. Diallo, I. O. Ryzhov, L. Yilmaz, S. Buckley, and J. A. Miller, eds, Savannah, Georgia, December 2014: 465-475.

Dufresne, D., Vázquez-Abad, F.J. (2013). Cobweb theorems with production lags and price forecasting. Economics: The Open-Access, Open-Assessment E-Journal 7 2013-23. http://dx.doi.org/10.5018/economics-ejournal.ja.2013-23

Bertoin, J., Dufresne, D., Yor, M. (2013). Some two-dimensional extensions of Bougerol's identity in law for the exponential functional of linear Brownian motion. Revista Matemática Iberoamericana 29(4): 1307-1324. Previous versions: http://arxiv.org/pdf/1201.1495.pdf; DufresneYor2011.pdf

Chin, S., and Dufresne, D. (2012). A general formula for option prices in a stochastic volatility model. Applied Mathematical Finance 19(4): 313-340. Previous version.

Dufresne, D. (2010). Stochastic volatility and option pricing. Risks and Rewards (Society of Actuaries) 55:28-31.

Dufresne, D. (2010). G distributions and the beta-gamma algebra. Electronic Journal of Probability 15: 2163-2199.

Dufresne, (2010). Beta products with complex parameters. Communications in Statistics - Theory and Methods 39: 837-854. Previous version.

Dufresne, D., Garrido, J., and Morales, M. (2009). Fourier inversion formulas in option pricing and insurance. Methodology and Computing in Applied Probability 11:359-383. Previous version.

Dufresne, D. (2008). Discounted claims in a renewal risk model Actuarial Research Clearing House 2009.1.

Dufresne, D. (2008). Sums of lognormals. Actuarial Research Clearing House: 2009.1.

Dufresne, D. (2007). Stochastic life annuities. North American Actuarial Journal 11: 136-157.

Dufresne, D. (2007). Fitting combinations of exponentials to probability distributions. Applied Stochastic Models in Business and Industry 23: 23-48. Previous version

Dufresne, D. (2005). Two notes in financial mathematics. Actuarial Research Clearing House: 2005.2.

Dufresne, D. (2005). Bessel processes and Asian options. In: Numerical Methods in Finance, H. Ben-Ameur and M. Breton (Editors.), Kluwer Academic Publisher.

Dufresne, D. (2004). The lognormal approximation in financial and other computations. Advances in Applied Probability 36: 747-773. Previous version

Dufresne, D. (2003). The integrated square-root process. 33 pages. Unpublished.

Chateau, J.P., and Dufresne, D. (2002). The stochastic-volatility American put option of banks' credit line commitments. International Review of Financial Analysis 11: 159-181.

Chateau, J.P., and Dufresne, D. (2002). Banks' regulatory capital requirement: Pricing the credit risk of short-term loan commitments. Proceedings of the Regulation and Deregulation of Financial Markets Conference, Principality of Liechtenstein, June 2002. Previous version

Dufresne, D. (2001). A decomposition of actuarial surplus. 22 pages. Unpublished.

Dufresne, D. (2001). On a general class of risk models. Australian Actuarial Journal 7: 755-791.

Dufresne, D. (2001). An affine property of the reciprocal Asian process. Osaka Journal of Mathematics 38: 379-381.

Dufresne, D. (2001). Some thoughts on the pricing of insurance liabilities. Magazine of the Actuarial Students' National Association 2001: 12-14.

Dufresne, D. (2001). The integral of geometric Brownian motion. Advances in Applied Probability 33: 223-241. Previous version

Bédard, D., and Dufresne, D. (2001). Pension funding with moving average rates of return. Scand. Actuarial J. 101: 1-17. Previous version

Dufresne, D. (2000). Laguerre series for Asian and other options. Mathematical Finance 10: 407-428. Previous version

Vazquez-Abad, F., and Dufresne, D. (1998). Accelerated simulation for pricing Asian options. Winter Simulation Conference Proceedings 2: 1493-1500.

Dufresne, D. (1998). Algebraic properties of beta and gamma distributions, and applications. Advances in Applied Mathematics 20: 285-299. Previous version

Chateau, J.P., and Dufresne, D. (1998). Valuing the stochastic volatility put option of banks' credit line commitments. Procedings of the International Conference of Finance, Association française de finance, Lille, France.

Boyle, P., Cox, S., Dufresne, D., Gerber, H., Mueller, H., Pederson, H., Pliska, S., Sherris, M., Shiu, E., and Tan, K.S. (1998). Financial Economics: With Applications to Investments, Insurance and Pensions. Actuarial Foundation, Chicago. 670 pages. (Commissioned by the Actuarial Foundation (Society of Actuaries, USA. Covers financial markets and derivatives, interest rate risk, immunization, no-arbitrage pricing, equilibrium pricing, term structure of interest rates, optimal portfolios.)

Alili, L., Dufresne, D., and Yor, M. (1997). Sur l'identité de Bougerol pour les fonctionnelles exponentielles du mouvement brownien avec drift. In: Exponential Functionals and Principal Values Related to Brownian Motion. Part A : Exponential Functionals, pp. 3-14. Biblioteca de la Revista Matematica Iberoamericana, Madrid.

Dufresne, D. (1997). Discussion of Z. Khorasanee's paper "Deterministic modelling of defined contribution pension funds". North American Actuarial Journal 1: 100-101.

Dufresne, D. (1996). Stochastic Calculus: A Tool for Finance. 70 pages. Unpublished.

Dufresne, D. (1996). From compound interest to Asian options. Quarterly Journal of the Institute of Actuaries of Australia 2: 2-17.

Dufresne, D. (1996). On the stochastic equation $ L(X) = L[B(X+C)]$ and a property of gamma distributions. Bernoulli 2: 287-291. Previous version

Dufresne, D. (1994). Mathématiques des caisses de retraite (Mathematics of Pension Funding). Éditions Supremum, Montreal. 200 pages. (Disponible sur demande.)

Dufresne, D. (1993). Some Aspects of Statement of Financial Accounting Standards No. 87. Project sponsored by the Actuarial Education and Research Fund. Actuarial Research Clearing House 1993.2: 1-130.

Dufresne, D. (1993). Current research on pension accounting. Actuarial Research Clearing House 1993.1: 321-331.

Dufresne, D. (1992). On discounting when rates of return are random. Transactions of the Twenty-Fourth International Actuarial Congress, Montreal, 1992, 1: 27-44.

Dufresne, D. (1992). Distributions of discounted values. Actuarial Research Clearing House 1992.1: 11-24.

Dufresne, D. (1991). Discussion of ``Stochastic life contingencies with solvency considerations'', by Edward Frees, Transactions of the Society of Actuaries 52: 131-145.

Dufresne, D. (1990). The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuarial J. 1990: 39-79.

Dufresne, D. (1990). Fluctuations of pension contributions and fund levels. Actuarial Research Clearing House 1990.1: 111-120.

Dufresne, D. (1989). Weak convergence of random growth processes with applications to insurance. Insurance: Mathematics and Economics 8: 187-201.

Dufresne, D. (1989). Stability of pension systems when rates of return are random. Insurance: Mathematics and Economics 8: 71-76.

Dufresne, D. (1988). Moments of pension contributions and fund levels when rates of return are random. Journal of the Institute of Actuaries 115: 535-544.

Dufresne, D. (1988). Comparison of funding methods in a static environment. Transactions of the Twenty-Third International Congress of Actuaries, Helsinki, Finland, 1988 2: 99-114.

Dufresne, D. (1986). Pension funding and random rates of return. In: Insurance and Risk Theory, M. Goovaerts, F. de Vylder, and J. Haezendonck (Editors), Proceedings of the NATO Advanced Study Institute, Maratea, Italy, 15-25 July, 1985.

Dufresne, D. (1986). The Dynamics of Pension Funding. PhD thesis, School of Actuarial Science and Statistics, The City University, London (England).