Equity Valuation, Hedging And Investing Based On Utility Function

The utility-based pricing and hedging are the central themes in the modern fi-nancial mathematics. In utility-based pricing two frameworks are the most important:the indiferent pricing(in the sense of Hodges and Neuberger[5]),and the neutral, oroptimal,pricing(in the sense of Kallsen[7]).In all of the above pricing and hedgingtopics, Pro.Srdjan Stojanovic elaborated in his recently published research monograph”Neutral and Indiference Portfolio Pricing, Hedging and Investing”[20],established themost powerful and the most feasible theorems. Indeed, the final results are fully de-rived pricing PDE systems and hedging formulas applicable for portfolios of contractsand for arbitrary difusive Markovian underlying models that are easy to implement onsymbolic computer platforms. The diference between the two pricing concepts abovecan be understood in the following way: the neutral(optimal)price is the low(high)priceat which one would ideally like to buy(sell),while the diference price is the price lim-it up(down)to which one would still go to close a particular deal. So,knowing bothprices is the best possibility, while if one is to choose between the two,although theindiference pricing is as of yet more widely known,the neutral(or optimal)pricing ismore informative.Futhermore,in the incomplete market,financial contracts portfolio in-vesting,neutral pricing with risk pre,indiference pricing,hedging can be solved in theMarkovian underlying models.This thesis research mainly on equity pricing and investing under diferent scenario.We employ CRRA utility of wealth and obtain the neutral(indiference)pricing. Firstof all, the investing portfolio optimization theory is introduced and then based on thetheory,the notation and the theorem of neutral pricing,diference pricing as well ashedging theory are described.Theme of the article is application and promotion of thetheory, and putting forward three equity pricing§investing model based on it.The firstmodel studies on the impact of equity dilution/buyback on the company’s stock price.We select accounting data as the factors. Stock price rely not only on book value,revenue, costs but also relates to the number of equity, therefore, compared to the basic pricing models, equity shares of the company is added as a factor to solve neutral(indiference) pricing problem. when solving partial diferential equations, ordinarydiferential equations are obtained. We found a explicit solution in a very special case,otherwise ODEs are solved by numerical methods.The results show that equity dilutionmakes the per share price down, and making the per share price up, but whetherdilution or buyback, the company’s total equity value is unchanged.The second modelconsiders how macroeconomic factors influence on the stock price. Two or three basicmacroeconomic factors are added and based on pricing theory neutral price is given.Feature of the model is that we put both China and the United States economic datainto the model to verify the model and then take the results back to the United Statesand other markets, in fact, the determination of model is closely related to the empiricalresults. we finalize the most realistic one by conducting a lot of empirical trying. Thethird model research on the optimal investment strategy of stock based on tradingvolume indicator, and use a lot of company accounting data to test on the results ofthe model. The model combined with the data we can obtain trading information suchas when to buy (or sell) and how much to buy (sell), and eventually it gets a verystable profit. Finally, neutral pricing of the corresponding futures are also considered.