We shall investigate the problem of optimal exercising strategy for option holders for the case in which option holders are averse to risk. A model of stock price changes incorporating the Lognormal random walk assumption will be combined with a class of utility functions containing diminishing marginal utility of money. In general, the strategy of waiting until the last possible day to exercise an option, which maximizes expected value, will not maximize expected utility. The strategy which maximizes expected utility is obtained by a dynamic programming formulation of the decision problem. At each day (or decision stage), the option holder may choose to act (exercise) or wait until the next day. Working backwards from the last day, a series of critical prices are obtained, with the optimal strategy being as follows: act if the stock price on any day is greater than the critical price for that day; otherwise, wait. Using the concept of proportional risk aversion developed by Pratt, we will demonstrate that, under certain conditions, a utility function which exhibits increasing proportional risk aversion is sufficient to create a series of finite critical prices. Moreover, once an option is exercised, the option holder continually faces a tactical decision to hold the stock and wait for capital gains or sell and take profits as ordinary income, thereby avoiding further risk. This decision may also be optimized by a dynamic programming scheme similar to the approach used above.

Inflation, Valuation, Accounting standards

Price-level costs, Historic costs, Questionnaire

Journal Article The Core of an Economy with a Measure Space of Economic Agents Get access W. Hildenbrand W. Hildenbrand University of California, Berkeley, U.S.A., Studiengruppe für Systemforschung, Heidelberg, Germany Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 35, Issue 4, October 1968, Pages 443–452, https://doi.org/10.2307/2296771 Published: 01 October 1968

Money, conventionally defined as demand deposits and currency held by the nonbank public, has two principal functions. It serves as a medium of exchange and as an asset conferring perfect liquidity on the holder.Savings deposits in commercial banks, savings and loan associations, mutual savings banks, credit unions, and the postal savings system are almost like money. For all practical purposes, they are perfectly liquid assets, or at least considered as such by depositors, and therefore substitutable for asset money. Because interest is paid on savings deposits, and not on demand deposits (except for an implicit return received through checking services provided below cost), it can be reasonably argued that the long-term asset demand for money (money that people expect to hold over six months) is considerably less than it would be in the absence of savings deposits. This does not mean, however, that the sum of currency, demand deposits, and savings deposits measures what the demand for money would be if savings deposits did not exist. Some savings deposits are certainly held in lieu of nonmonetary assets.

Journal Article Reaction Functions and the Theory of Duopoly Get access J. W. Friedman J. W. Friedman Yale University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 35, Issue 3, July 1968, Pages 257–272, https://doi.org/10.2307/2296661 Published: 01 July 1968

Journal Article Linear Decision Rules for Economic Stabilization and Growth: Comment Get access W. Lynn Holmes W. Lynn Holmes Temple University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 82, Issue 3, August 1968, Pages 514–518, https://doi.org/10.2307/1879524 Published: 01 August 1968

The role of speculative short term capital movements in balance of payments adjustment and in exchange market stability is examined. A theory of speculative behavior with a distributed lag model of expectation formation at its core is developed and empirically tested using the Canadian data for the period 1952-1960. Tests of an alternative but generically similar specification of the model are also presented and discussed.