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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 12

Risk-Neutral Pricing in the (B, S) Economy: One Underlying Stock

At this point we have the necessary tools in stochastic analysis for developing the theory of derivative pricing and hedging in continuous time in an economy where risky assets are modelled as Itô processes. In this chapter we consider an economy with two securities: a single tradable risky asset, namely, a stock, and a money market (bank) account or a bond. We refer to this as a (B, S) economy with only two tradable assets: B stands for the bank account or bond and S stands for the stock. More specifically, this chapter is devoted to presenting the theoretical framework solely within the classical case of an economy where the interest rate is fixed and the stock price ...

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