Mean-Variance Portfolio Selection Accounting for Financial Bubbles: A Mean-Field Type Approach

Abstract: The phenomenon of financial bubbles is known to have impacted various markets since the seventeenth century. Such bubbles are known to form when the market drastically overvalues the price of an asset, causing its market value to increase hyperbolically, only to suddenly collapse once the untenable perceived future prospects of the asset are realized. Hence, it remains crucial for investors to be able to sell off assets residing within a bubble before they burst and their value is significantly diminished. Thus, portfolio optimization methods capable of accounting for financial bubbles in stock dynamics is a field of great value and interest for market participants. Portfolio optimization with respect to the mean-field is a relatively novel approach to accounting for the bubble-phenomenon. Hence, this paper investigates a previously unattempted method of portfolio optimization, providing a mean-field solution to the mean-variance trade-off problem, as well as providing new definitions of stock dynamics capable of diverting investors from bubbles.