By Alexandre Ziegler
This booklet offers a style that mixes online game thought and alternative pricing so one can research dynamic multiperson determination difficulties in non-stop time and below uncertainty. the fundamental instinct of the tactic is to split the matter of the valuation of payoffs from the research of strategic interactions. while the previous is to be dealt with utilizing alternative pricing, the latter may be addressed by means of video game thought. The textual content indicates how either tools might be mixed and the way video game idea should be utilized to complicated difficulties of company finance and fiscal intermediation. along with supplying theoretical foundations and serving as a advisor to stochastic online game idea modeling in non-stop time, the textual content comprises various examples from the speculation of company finance and fiscal intermediation. via combining arbitrage-free valuation suggestions with strategic research, the sport concept research of concepts truly presents the hyperlink among markets and firms.
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Extra info for A Game Theory Analysis of Options: Contributions to the Theory of Financial Intermediation in Continuous Time
6 derives the optimal capital structure and discusses its properties. 7 develops an incentive contract aiming at realizing a prespecified bankruptcy behavior of the borrower. 8 presents an extension of the model to a different payout setting. 9 summarizes the main results and insights of the chapter. Financing Decision Interest Rates r* and ifJ Amount of Debt D ~ Investment Decision Underinvestment? 1: Structure of the game. In the first phase, lender and borrower sign a contract specifying the face amount of debt, D, and the interest rates r* and ifJ.
5) The general solution is (6) where 1 2 See Merton (1990), p. 298. From the definitions in equations (3) and (4), Fs =G', Fss =G" / D, FD = G - VG' . Substituting these expressions into (2) yields G" ta 2 S 2 -+rSG' +r* D(G - VG') - rDG +l/JD=O. D Collecting terms and crossing out D gives (5). See Ingersoll (1987), p. 380 for an example of this method. 3 The Value o/the Firm and its Securities 37 r-r* r*=2--. (12 (7) Substituting the original variables back into (6) yields the following expression for the value of the debt, F: F=aoD(t)+a1S+a2 ( D(t)) l+y* * s-y.
To interpret equation (15) more easily, one can rewrite it as 3. Endogenous Bankruptcy and Capital Structure 38 (S J- *) q,D(t) ( 1- F(S)=-r-r* SB Y ( SJ- * +(1-a)SB . SB Y (16) Equation (16) says that the value of the risky debt equals the value of the risk-free debt, q,D(t) I (r - r*), times the risk-neutral probability that bankruptcy does not occur, 1- (S I S B) -y* , plus the value of the proceeds from asset liquidation in the event of bankruptcy, (1- a)S B' times the risk-neutral probability of bankruptcy, (S I S B) -y* .
A Game Theory Analysis of Options: Contributions to the Theory of Financial Intermediation in Continuous Time by Alexandre Ziegler