In this online appendix we provide proofs and additional results to the paper “A Dynamic Model of Altruistically-Motivated Transfers”.

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Online Appendix to: A Dynamic Model of Altruistically-Motivated Transfers

The assumption that government bonds are perceived as net wealth by the private sector is crucial in demonstrating real effects of shifts in the stock of public debt. In particular, the standard effects of "expansionary" fiscal policy on aggregate demand hinge on this assumption. Government bonds will be perceived as net wealth only if their value exceeds the capitalized value of the implied stream of future tax liabilities. This paper considers the effects on bond values and tax capitalization of finite lives, imperfect private capital markets, a government monopoly in the production of bond "liquidity services," and uncertainty about future tax obligations. It is shown within the context of an overlapping-generations model that finite lives will not be relevant to the capitalization of future tax liabilities so long as current generations are connected to future generations by a chain of operative intergenerational transfers (either in the direction from old to young or in the direction from young to old). Applications of this result to social security and to other types of imposed intergenerational transfer schemes are also noted. In the presence of imperfect private capital markets, government debt issue will increase net wealth if the government is more efficient, at the margin, than the private market in carrying out the loan process. Similarly, if the government has monopoly power in the production of bond "liquidity services," then public debt issue will raise net wealth. Finally, the existence of uncertainty with respect to individual future tax liabilities implies that public debt issue may increase the overall risk contained in household balance sheets and thereby effectively reduce household wealth.(This abstract was borrowed from another version of this item.)

/pdf/are-government-bonds-net-wealth-3n21dugw99.pdf

Are Government Bonds Net Wealth

Some Mathematical Preliminaries.- Ito Integrals.- The Ito Formula and the Martingale Representation Theorem.- Stochastic Differential Equations.- The Filtering Problem.- Diffusions: Basic Properties.- Other Topics in Diffusion Theory.- Applications to Boundary Value Problems.- Application to Optimal Stopping.- Application to Stochastic Control.- Application to Mathematical Finance.

Stochastic differential equations : an introduction with applications

This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through illustrative examples and selective material, to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance. In this Second Edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.

/pdf/controlled-markov-processes-and-viscosity-solutions-4n8p6ywj5v.pdf

Controlled Markov processes and viscosity solutions

Publisher Summary This chapter examines viscosity solutions of Hamilton–Jacobi equations. The ability to formulate an existence and uniqueness result for generality requires the ability to discuss non differential solutions of the equation, and this has not been possible before. However, the existence assertions can be proved by expanding on the arguments in the introduction concerning the relationship of the vanishing viscosity method and the notion of viscosity solutions, so users can adapt known methods here. The uniqueness is then the main new point.

https://www.ams.org/tran/1983-277-01/S0002-9947-1983-0690039-8/S0002-9947-1983-0690039-8.pdf

Viscosity solutions of Hamilton-Jacobi equations

Traditionally, household behavior is derived from the maximization of a unique utility function. In this paper, we propose an alternative approach, in which the household is modeled as a two-member collectivity taking Pareto-efficient decisions. The consequences of this assumption are analyzed in a three-good model, in which only total consumption and each member's labor supply are observable. If the agents are assumed egoistic (i.e., they are only concerned with their own leisure and consumption), it is possible to derive falsifiable conditions upon household labor supplies from both a parametric and nonparametric viewpoint. If, alternatively, agents are altruistic, restrictions obtain in the nonparametric context; useful interpretation stems from the comparison with the characterization of aggregate demand for a private-good economy.

Online Appendix to: A Dynamic Model of Altruistically-Motivated Transfers

References

Are Government Bonds Net Wealth

Stochastic differential equations : an introduction with applications

Controlled Markov processes and viscosity solutions

Viscosity solutions of Hamilton-Jacobi equations

Rational household labor supply

Related Papers (1)

Online Appendix to "A Dynamic Model of Altruistically-Motivated Transfers"