In 1981, Paris and Wilkie [28] indicated it was an open question whether IΣ0 would satisfy the Second Incompleteness Theorem for Herbrand deduction. We will show that some specially formulated axiomizations for IΣ0 can evade the Herbrandized version of the Second Incompleteness Theorem.

Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ b...

The aim of this paper is to examine the concentration of wealth among the group of top wealth holders, defined as those with wealth in excess of a high cut off. The paper begins by considering the definition of this cut off, analogous to the definition of a poverty line at the other end of the distribution. It then considers what can be learned about the proportion classified as ‘rich’ and abou...

We begin the development of a theory of Banach spaces in the definable setting of o-minimal structures. We outline several results which develop the theory of compact embeddings for explicitly given function spaces. One aim is to explain the substantive underpinnings of an important observation used in the proof of the Reparameterization Theorem of Pila and Wilkie in [2]. We place this observat...

Public cooperation plays a significant role in the survival and maintenance of biological species, to elucidate its origin thus becomes an interesting question from various disciplines. Through long-term development, the public goods game has proven to be a useful tool, where cooperator making contribution can beat again the free-rides. Differentiating from the traditional homogeneous investmen...

Policyholder exercise behavior presents an important risk factor for pricing Variable Annuities. However, approaches presented in the literature—building on value-maximizing strategies akin to American options—do not square with observed price and patterns popular withdrawal guarantees. We show that including taxes into valuation closes this gap between theory practice. In particular, we develo...

Variable annuity is a retirement planning product that allows policyholders to invest their premiums in equity funds. In addition to the participation in equity investments, the majority of variable annuity products in today’s market offer various types of investment guarantees, protecting policyholders from the downside risk of their investments. One of the most popular investment guarantees i...

The recent market downturn highlighted the substantial impact that capital markets fluctuations can have on retirement wealth. A possible strategy to manage investment risk is to purchase guarantees (i.e. put options), which can be fairly expensive. As an alternative, this paper suggests that an individual can self-insure against poor market outcomes by adjusting his retirement date as a functi...

Implicit guarantees provided by financial intermediaries are a key component of China's shadow banking sector. We show theoretically that project screening intermediaries, accompanied their implicit to investors, can be the second-best arrangement and mitigate capital misallocation favors state-owned enterprises (SOEs). Using dataset trusts’ investment products, we find, consistent with our mod...