Abstract
This study formulates a dynamic model of a household’s asset-formation process under stochastic arrivals of disasters. If the disaster risk is catastrophic, then the disaster insurance market cannot spread the risk completely, and the insurance premium will include additional loadings, namely, risk premiums. The study reports that, under such a market condition, the representative household does not purchase an insurance that fully covers its potential losses, resulting in a non-smooth asset-formation path that is associated with downward jumps at times of disaster. It concludes that the benefit of disaster mitigation investment is thus composed of an “ex ante accumulation effect” and an “ex post mitigation effect.” The dynamic problem of a household’s asset formation is characterized by the jump control problem related to insurance contracts. Moreover, the problem is associated with a recursive structure where a phase of recovery from one disaster is simultaneously a phase of preparedness for the next disaster that randomly arrives; thus, extra attention is given to optimal resource allocation between reconstruction and risk management. The jump control model can be a new standard mathematical framework of household resilience.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aase KK (1984) Optimum portfolio diversification in a general continuous-time model. Stoch. Process Appl 18(1):81–98
Aghion P, Howitt P (1990) A model of growth through creative destruction. Technical report, National Bureau of Economic Research
Aghion P, Ljungqvist L, Howitt P, Howitt PW, Brant-Collett M, García-Peñalosa C et al (1998) Endogenous growth theory. MIT press
Aït-Sahalia Y, Cacho-Diaz J, Hurd TR, et al (2009) Portfolio choice with jumps: a closed-form solution. Ann Appl Probab 19(2):556–584
Wouter Botzen WJ, van den Bergh JCJM (2012) Risk attitudes to low-probability climate change risks: Wtp for flood insurance. J Econ Behav Organiz 82(1):151–166
Bruneau M, Chang SE, Eguchi RT, Lee GC, O’Rourke TD, Reinhorn AM, Shinozuka M, Tierney K, Wallace WA, Von Winterfeldt D, (2003) A framework to quantitatively assess and enhance the seismic resilience of communities. Earthquake spectra 19(4):733–752
Chao-lin H (2010) Dynamic portfolio choice: Time-varying and jumps. In: 2010 IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS), vol 1. IEEE, pp 507–511
Diamond PA, Mirrlees JA (2008) 11 insurance aspects of pensions. In: Pensions, labor, and individual choice, p 317
Fisher I (1906) The nature of capital and income. The Macmillan Company
Green JR (1985) The riskiness of private pensions. In: Pensions, labor, and individual choice. University of Chicago Press, pp 357–378
Grossman GM, Helpman E (1991) Quality ladders in the theory of growth. Rev Econ Stud 58(1):43–61
Hicks JR (1939) The foundations of welfare economics. Econ J 49(196):696–712
Kallsen J (2000) Optimal portfolios for exponential lévy processes. Math Methods Oper Res 51(3):357–374
Kiyotaki N, Wright R (1991) A contribution to the pure theory of money. J Econ Theory 53(2):215–235
Klein RJT, Nicholls RJ, Thomalla F (2003) Resilience to natural hazards: how useful is this concept? Global Environ Change Part B: Environ Hazards 5(1):35–45
Kobayashi K, Yokomatsu M (2000) Catastrophe risks and economic valuation of disaster prevention investment. JSCE J Infrastruct Planning Manag (in Japanese) 639:39–52
Manyena SB (2006) The concept of resilience revisited. Disasters 30(4):434–450
Merton R (1971) Optimal portfolio and consumption rules in a continuous-time model. J Econ Theory 3(4):373–413
Mitchell A (2013) Risk and resilience
Modigliani F (1966) The life cycle hypothesis of saving, the demand for wealth and the supply of capital. In: Social Research, pp 160–217
Moen ER (1997) Competitive search equilibrium. J Politic Econ 105(2):385–411
Paton D, Johnston D (2001) Disasters and communities: vulnerability, resilience and preparedness. Disaster Prevent Manag: Int J 10(4):270–277
Phelps ES (1962) The accumulation of risky capital: a sequential utility analysis. Econ: J Econ Soc 729–743
Richard SF (1975) Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model. J Financial Econ 2(2):187–203
Rose A (2004) Defining and measuring economic resilience to disasters. Disaster Prevent Manag: Int J 13(4):307–314
Steger TM (2005) Stochastic growth under wiener and poisson uncertainty. Econ Lett 86(3):311–316
Tobin GA (1999) Sustainability and community resilience: the holy grail of hazards planning? Global Environ Change Part B: Environ Hazards 1(1):13–25
UNISDR (2005) Hyogo framework for action 2005–2015
UNO UNISDR (2015) Sendai framework for disaster risk reduction 2015–2030. In 3rd United Nations world conference on DRR. UNISDR Sendai, Japan
Wälde K (2005) Endogenous growth cycles. Int Econ Rev 46(3):867–894
Yaari ME (1965) Uncertain lifetime, life insurance, and the theory of the consumer. Rev Econ Stud 32(2):137–150
Yokomatsu M (2018) A commentary on grecovery from catastrophe and building back better (Takeuchi and Tanaka, 2016)h-structure of damage of production capital stock on normative economic process. J Disaster Res 13(3):564–570
Yokomatsu M, Kobayashi K (1999) The economic benefit of irreversible risk reduction by disaster prevention investment. In: 1999 IEEE international conference on systems, man and cybernetics, vol 5. IEEE, pp 979–984
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Yokomatsu, M., Kobayashi, K. (2020). Disaster Risk and a Household’s Dynamic Asset-Formation Behavior: Jump Control Model of Household. In: Yokomatsu, M., Hochrainer-Stigler, S. (eds) Disaster Risk Reduction and Resilience. Disaster and Risk Research: GADRI Book Series. Springer, Singapore. https://doi.org/10.1007/978-981-15-4320-3_6
Download citation
DOI: https://doi.org/10.1007/978-981-15-4320-3_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-4319-7
Online ISBN: 978-981-15-4320-3
eBook Packages: Social SciencesSocial Sciences (R0)