zbMATH — the first resource for mathematics

On barrier strategy dividends with Parisian implementation delay for classical surplus processes. (English) Zbl 1231.91430
Summary: We apply a single barrier strategy to optimise dividend payments in the situation where there is a time lag $$d>0$$ between decision and implementation. Using a classical surplus process with exponentially distributed jumps, we obtain the optimal barrier $$b^{\ast }$$ which maximises the expected present value of dividends.

MSC:
 91G20 Derivative securities (option pricing, hedging, etc.)
Full Text:
References:
 [1] Arfken, G., Mathematical methods for physicists, (1970), Academic Press · Zbl 0135.42304 [2] Asmussen, S.; M., Taksar, Controlled diffusion models for optimal dividend pay-out, Insurance: mathematics and economics, 20, 1-15, (1997) · Zbl 1065.91529 [3] Bar-Ilan, A.; Strange, C., Investment lags, The American economic review, 86, 610-622, (1996) [4] Beteman, H., Table of integral transforms, vol. I, (1954), McGraw-Hill book company, INC [5] Bühlmann, H., Mathematical methods in risk theory, (1970), Springer, (Reprinted 1996) · Zbl 0209.23302 [6] Chesney, M.; Jeanblanc-Picqué, M.; Yor, M., Brownian excursions and Parisian barrier options, Advances in applied probability, 29, 165-184, (1997) · Zbl 0882.60042 [7] Claramunt, M.; Marmol, M.; Alegre, A., A note on the expected present value of dividends with a constant barrier in the discrete time model, Bulletin of the swiss association of actuaries, 149-159, (2003) · Zbl 1333.91021 [8] Costeniuc, M., Schnetzer, M., Taschini, L., 2009. Entry and exit decision problem with implementation delay, Advances in Applied Probability (in press) · Zbl 1167.60008 [9] Dassios, A., Wu, S., 2009. Perturbed Brownian motion and its application to Parisian option pricing, Finance and Stochastics (in press) · Zbl 1226.91073 [10] Dassios, A., Wu, S., 2008a. Brownian excursions outside a corridor and two-sided Parisian options. Working paper L.S.E [11] Dassios, A., Wu, S., 2008b. Brownian excursions in a corridor and related Parisian options. Working paper L.S.E [12] Dassios, A., Wu, S., 2008c. Parisian options and Parisian ruin with exponential claims. Working paper L.S.E [13] De Finetti, Bruno, Su un’ impostazione alternativa dell teoria collettiva del rischio, Transactions of the xvth international congress of actuaries, 2, 433-443, (1957) [14] Frostig, E., The expected time to ruin in a risk process with constant barrier via martingales, Insurance: mathematics and economics, 37, 216-228, (2005) · Zbl 1117.91381 [15] Gauthier, L.; Morellec, E., Investment under uncertainty with implementation delay, () [16] Gerber, H.U., () [17] Gerber, H.U.; Shiu, E.S.W., Optimal dividends: analysis with Brownian motion, North American actuarial journal, 8, 1-20, (2004) · Zbl 1085.62122 [18] Gerber, H.U.; Shiu, E.S.W., Geometric Brownian motion models for assets and liabilities: from pension funding to optimal dividends, North American actuarial journal, 3, 37-51, (2003) · Zbl 1084.91517 [19] Jeanblanc-Picqué, M.; Shiryaev, A.N., Optimization of the flow of dividends, Russian mathematical surveys, 20, 257-277, (1995) · Zbl 0878.90014 [20] Hartley, P., Pricing Parisian options by Laplace inversion, Decisions in economics and finance, (2002) [21] Højgaard, B., Optimal dynamic premium control in non-life insurance. maximizing dividend pay-outs, Scandinavian actuarial journal, 225-245, (2002) · Zbl 1039.91042 [22] Højgaard, B.; Taksar, M., Controlling risk exposure and dividends payout schemes: insurance company example, Mathematical finance, 9, 153-182, (1999) · Zbl 0999.91052 [23] Labart, C., Lelong, J., Dec 2005. Pricing Parisian options, Technical report, ENPC. http://cermics.enpc.fr/reports/CERMICS-2005/CERMICS-2005-294.pdf · Zbl 1190.91143 [24] Liu, X.S.; Willmot, G.E.; Drekic, S., The compound Poisson risk model with a constant dividend barrier: analysis of the gerber – shiu penalty function, Insurance: mathematics and economics, 33, 551-566, (2003) · Zbl 1103.91369 [25] Paulsen, J.; Gjessing, H.K., Optimal choice of dividend barriers for a risk process with stochastic return on investments, Insurance: mathematics and economics, 20, 215-223, (1997) · Zbl 0894.90048 [26] Schmidli, H., Stochastic control in insurance, (2008), Springer · Zbl 1133.93002 [27] Shreve, S.E.; Lehoczky, J.P.; Gaver, D.P., Optimal consumption for general diffusions with absorbing and reflecting barriers, SIAM journal on control and optimization, 22, 55-75, (1984) · Zbl 0535.93071 [28] Wang, N.; Politis, K., Some characteristic of a surplus process in the presence of an upper barrier, Insurance: mathematics and economics, 30, 231-241, (2002) · Zbl 1055.91058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.