Ir al contenido

Documat

Stochastic cash flows modelled by homogeneous and non-homogeneous discrete time backward semi-Markov reward processes

  • Autores: Fulvio Gismondi, Jacques Janssen, Raimondo Manca, Ernesto Volpe di Prignano
  • Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 38, Nº. 2, 2014, págs. 107-138
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The main aim of this paper is to give a systematization on the stochastic cash flows evolution. The tools that are used for this purpose are discrete time semi-Markov reward processes. The paper is directed not only to semi-Markov researchers but also to a wider public, presenting a full treatment of these tools both in homogeneous and non-homogeneous environment. The main result given in the paper is the natural correspondence of the stochastic cash flows with the semi-Markov reward processes. Indeed, the semi-Markov environment gives the possibility to follow a multi-state random system in which the randomness is not only in the transition to the next state but also in the time of transition. Furthermore, rewards permit the introduction of a financial environment into the model. Considering all these properties, any stochastic cash flow can be naturally modelled by means of semi-Markov reward processes. The backward case offers the possibility of considering in a complete way the duration inside a state of the studied system and this fact can be very useful in the evaluation of insurance contracts.

  • Referencias bibliográficas
    • Artikis, T. P. and Malliaris, A. G. (1990). Discounting certain random sums. Scandinavian Actuarial Journal, 1-2, 34–38.
    • Artikis, T. and Voudouri, A. (2000). A stochastic integral arising in discounting continuous cash flows and certain transformed characteristic...
    • Balcer, Y. and Sahin, I. (1979). Stochastic models for a pensionable service. Operations Research, 27, 888– 903.
    • Balcer, Y. and Sahin, I. (1986). Pension accumulation as a semi-Markov reward process, with applications to pension reform. Semi-Markov models....
    • Beekman, J. A. and Fuelling, C. P. (1991). Extra randomness in certain annuity models. Insurance Mathematics and Economics, 10, 275–287.
    • Browne, S. (1995). Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of...
    • Carravetta, M., De Dominicis, R. and Manca, R. (1981). Semi-Markov stochastic processes in social security problems. Cahiers du C.E.R.O.,...
    • CMIR12 (1991). (Continuous Mortality Investigation Report, number 12). The analysis of permanent health insurance data. The Institute of Actuaries...
    • D’Amico, G., Guillen, M. and Manca, R. (2009). Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya...
    • D’Amico, G., Guillen, M. and Manca, R. (2013). Semi-Markov Disability Insurance Models. Communications in Statistics-Theory and Methods, 42,...
    • D’Amico, G., Janssen, J. and Manca, R. (2009a). The dynamic behavior of single unireducible nonhomogeneous Markov and semi-Markov chains....
    • De Dominicis, R. and Manca, R. (1986). Some new results on the transient behaviour of semi-Markov reward processes. Methods of Operations...
    • De Medici, G., Janssen, J. and Manca, R. (1995). Financial operation evaluation: a semi-Markov approach. Proc. V AFIR Symposium Brussels,...
    • De Schepper, A. and Goovaerts, M. (1992). Some further results on annuities certain with random interest rate. Insurance Mathematics and Economics,...
    • De Schepper, A., Teunen, M. and Goovaerts, M. (1994). An analytical inversion of a Laplace transform related to annuities certain. Insurance...
    • Donati-Martin, C., Matsumoto, H. and Yor, M. (2000). On positive and negative moments of the integral of geometric Brownian motions. Statistics...
    • Duffie, D., Pan, J. and Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68, 1343–1376.
    • Dufresne, D. (2001). The integral of geometric Brownian motion. Advances in Applied Probability, 33, 223–241.
    • Estes, J. H., Moor, W. C. and Rollier, D. A. (1989). Stochastic cash flow evaluation under conditions of uncertain timing. Engineering Costs...
    • Haberman, S. and Pitacco, E. (1999). Actuarial Models for Disability Insurance, Chapman & Hall.
    • Halliwell, L. J. (2003). The Valuation of Stochastic Cash Flows. CAS Forum, (Reinsurance Call Papers, Spring 2003), 1-68, available on line...
    • Harrison, M. J. (1977). Ruin problems with compounding assets. Stochastic Processes and their Applications, 5, 67–79.
    • Hoem, J. M. (1972). Inhomogeneous semi-Markov processes, select actuarial tables, and duration-dependence in demography. In Population, Dynamics,...
    • Howard, R. (1971). Dynamic probabilistic systems, vol II, Wiley.
    • Janssen, J. (1966). Application des processus semi-markoviens à un probléme d’invalidité. Bulletin de l’Association Royale des Actuaries...
    • Janssen, J. and Manca, R. (1997). A realistic non-homogeneous stochastic pension funds model on scenario basis. Scandinavian Actuarial Journal,...
    • Janssen, J. and Manca, R. (1998). Non-homogeneous stochastic pension fund model: an algorithmic approach. Transactions of the 26th ICA Birmingham...
    • Janssen, J. and Manca, R. (2002). General actuarial models in a semi-Markov environment. Proceedings of 27th ICA 2002, Cancun, available on...
    • Janssen, J. and Manca, R. (2006). Applied semi-Markov Processes, Springer.
    • Janssen, J. and Manca, R. (2007). Semi-Markov Risk Models for Finance, Insurance and Reliability, Springer.
    • Janssen, J. and Manca, R. and Volpe di Prignano, E.(2002). Non homogeneous interest rate structure in a semi-Markov framework. Proceedings...
    • Janssen, J. and Manca, R. and Volpe di Prignano, E. (2004). Continuous Time Non Homogeneous SemiMarkov a. Reward Processes And Multi-State...
    • Janssen, J. and Manca, R. and Volpe di Prignano, E. (2009). Mathematical Finance, Deterministic and Stochastic models, ISTE Wiley.
    • Limnios, N. and Oprişan, G. (2001). Semi-Markov Processes and Reliability, Birkhäuser, Boston.
    • Marocco, P. and Pitacco, E. (1998). Longevity risk and life annuity reinsurance. Transactions of the 26th ICA Birmingham, vol VI, 453–479.
    • Milevsky, M. (1997). The present value of a stochastic perpetuity and the gamma distribution. Insurance Mathematics and Economics, 20, 243–250.
    • Milevsky, M. and Posner, E. (1998). Asian options, the sum of lognormals and the reciprocal gamma distribution. Journal of Financial and Quantitative...
    • Papadopoulou, A. A. (2013). Some results on modeling biological sequences and web navigation with a semi-Markov chain. Communications in statistics-Theory...
    • Papadopoulou, A. A. and Tsaklidis, G. M. (2007). Some reward paths in semi-Markov models with stochastic selection of the transition probabilities....
    • Papadopoulou, A. A., Tsaklidis, G., McClean, S. and Garg, L. (2012). On the moments and the distribution of the cost of a semi-Markov model...
    • Parker, G. (1994). Limiting distribution of the present value of a portfolio. Astin Bulletin, 24, 47–60.
    • Perry, D. and Stadje, W. (2000). Risk analysis for a stochastic cash management model with two types of customers. Insurance Mathematics and...
    • Perry, D. and Stadje, W. (2001). Function space integration for annuities. Insurance Mathematics and Economics, 29, 73–82.
    • Pitacco, E. and Olivieri, A. (1997). Introduzione alla teoria attuariale delle assicurazioni di persone, Quaderno UMI, 42.
    • Pliska, S. R. (1986). A stochastic calculus model of continuous trading. Mathematics of Operations Research, 11, 371–382.
    • Qureshi, M. A. and Sanders, H. W. (1994). Reward model solution methods with impulse and rate rewards: an algorithmic and numerical results....
    • Papadopoulou, A. A., Tsaklidis, G., McClean, S. and Garg, L. (2012). On the moments and the distribution of the cost of a semi-Markov model...
    • Sato, S. and Yor, M. (1998). Computation of moments for discounted Brownian additive functional. Journal of Mathematics of Kioto University,...
    • Silvestrov, D. S. (1980). Semi-Markov Processes with a Discrete State Space, Sovetske Radio, Moskow (Russian).
    • Stenberg, F., Manca, R. and Silvestrov, D. (2006). Semi-Markov reward models for insurance. Theory of Stochastic Processes, 12, 239–254.
    • Stenberg, F., Manca, R. and Silvestrov, D. (2007). An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward processes...
    • Swishchuk, A. V. (1995). Hedging of options under mean-square criterion and with semi-Markov volatility. Ukrainian Mathematic Journal, 47,...
    • Vanneste, M., Goovaerts, M. J., De Schepper, A. and Dhaene, J. (1997). A straightforward analytical calculation of the distribution of an...
    • Vanneste, M., Goovaerts, M. J. and Labie, E. (1994). The distribution of annuities. Insurance Mathematics and Economics, 15, 37–48.
    • Wilkie, A. D. (1986). A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–403.
    • Wilkie, A. D. (1995). The risk premium on ordinary shares (with discussion). British Actuarial Journal, 1, 251–293.
    • Wolthuis, H. (2003). Life Insurance Mathematics (the Markovian Model), II edition, Peeters Publishers, Herent. XI, 288.
    • Yntema, L. (1962). Amarkovian treatment of silicosis. Acta III Conferencia Int. De Actuarios y Estadı́sticos de la Seguridad Social, Madrid.
    • Yor, M. (2001). Exponential Functionals of Brownian Motion and Related Processes, Springer.
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno