Browsing by Author "Pinar, M. Ç."

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    The Best Gain-Loss Ratio is a Poor Performance Measure
    (Society for Industrial and Applied Mathematics, 2013-03-06) Biagini, S.; Pinar, M. Ç.
    The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index, and we provide its dual representation for general probability spaces. However, the gain-loss ratio was designed for finite Ω and works best in that case. For general Ω and in most continuous time models, the best gain-loss is either infinite or fails to be attained. In addition, it displays an odd behavior due to the scale invariance property, which does not seem desirable in this context. Such weaknesses definitely prove that the (best) gain-loss is a poor performance measure.
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    Pricing American perpetual warrants by linear programming
    (Society for Industrial and Applied Mathematics, 2009) Vanderbei, R.J.; Pinar, M. Ç.
    A warrant is an option that entitles the holder to purchase shares of a common stock at some prespecified price during a specified interval. The problem of pricing a perpetual warrant (with no specified interval) of the American type (that can be exercised any time) is one of the earliest contingent claim pricing problems in mathematical economics. The problem was first solved by Samuelson and McKean in 1965 under the assumption of a geometric Brownian motion of the stock price process. It is a well-documented exercise in stochastic processes and continuous-time finance curricula. The present paper offers a solution to this time-honored problem from an optimization point of view using linear programming duality under a simple random walk assumption for the stock price process, thus enabling a classroom exposition of the problem in graduate courses on linear programming without assuming a background in stochastic processes.