Research

Forward-looking Statements in MD&As by P&C Insurance Companies

Supervised by Dr. Martin Grace

Working Paper 2021

This study examines the information content of forward-looking statements (FLS) in the Management's Discussion and Analysis (MD&A) section of P&C insurance companies' annual filings to NAIC. Using a structural topic model to classify the topics contained in the forward-looking sentences in MD&A sections, we find that these forward-looking sentences can predict earnings management and different aspects of future performance. And more topics are significantly related to future expenses, losses than earnings. The absolute value of performance measures has higher predictability than the relative annual changes. And the forward-looking sentences have better explanatory power for a new forward-looking reserve error measure. In addition, we find that organizational form incentives firms to provide different disclosures.

Linear Models with Distributed Data and Communication-Efficient Estimator: Limiting Distribution and Its Approximation

Ziyan Yin, Cheng Yong Tang, and Jian Zhang

Submitted to JMLR, 2021

In current large-scale practical investigations, it is common that data are distributed in multiple parallel centers. For reasons including confidentiality concerns, the data from every center are not all available when conducting statistical analysis. To solve the data-enabled problems more efficiently in this scenario, a class of communication-efficient methods are being actively developed. We investigate in this study the limiting distribution of the estimators that requires a one-step updating, combining data information transferred from all parallel centers. Our analysis reveals that the number of centers is a critical issue. In particular, when the number of centers is not small compared with the sample size at the local center, a non-negligible impact occurs in the limiting distribution. Moreover, we find that the limiting distribution itself is interesting – it is a mixture involving a product of normal random variables. As a result, conventional methods for statistical inferences by only incorporating the variance estimations may be severely biased – leading to serious under-coverage. Based on our analysis, we then propose a multiplier-bootstrap method for approximating the distribution of the estimator. To meet the challenges in high-dimensional problems, we further develop a data-splitting and re-fitting strategy to handle the limiting distribution therein. Our theory and extensive numerical examples confirm the validity and promising performance of the proposed new approaches.

Insurance and Self-protection for Increased Risk Aversion

Jingyuan Li, Jianli Wang, and Jian Zhang

Working Paper, 2017

We re-examine the classic problem of risk aversion and self-protection in this paper. In the beginning of this paper, we conduct comparative statics of risk aversion and prevention efforts based on the mono-periodic two states model of choice under risk. We show this new condition is effective with self-insurance -cum-protection model (Lee, 1998), in which the decision maker’s activities to prevent the risk can sever both as self-insurance and self-protection. We suggest a new condition that increased risk aversion induces more prevention activities. This new condition requires only one assumption concerning fear of ruin coefficient, the marginal effect of SICP activity on probability and the marginal cost of SICP activity. By applying interval dominance order (Quah and Strulovici,2009), we find that a decision-maker will exert a higher level of SICP activity if he becomes more risk-averse, under the condition that his hazard rate is higher than the ’boldness’ coefficient (Aumann and Kurz,1977). This new condition is effective even when the optimal level for SICP activity is not interior solution. With our method, the assumption, that the optimal solution is interior, is not necessary, and marginal utility functions do not need to be monotonic on the interval [0, w]. Based on this, the optimal solution can be a corner solution or inflection point solution. And the DM’s attitude towards risk can be variable. Hence, the relation suggested by our findings is more consistent with real-world situations.