(Update 24-8-2014: Added things on Markov Chains).
I doubt that there is a single "textbook" that covers all this. So partial suggestions for just three of these topics:
For Markov Chains, I provide first two math.SE links that contain many suggestions:
https://math.stackexchange.com/questions/15431/good-introductory-book-for-markov-processes
and
https://math.stackexchange.com/questions/27514/nice-references-on-markov-chains-processes/27516#27516
I was able to refresh some of these texts, and they confirmed my impression that Markov Chain books are always much more advanced mathematics than anything else (sometimes, not even the Introduction contains more words than mathematical symbols).
It appears that the most accessible (relatively speaking) is "Markov Chains and Mixing Times" (2008) by D.A. Levin, Y. Peres, and El.L.Wilmer, which is also officially available for download (with a separate file with Errata). At least it contains a picture with a frog in the first page of the first chapter, and the general title of Part II of the book is "The Plot Thickens" -so we have been given fair warning.
For MarkovChainMonteCarlo, if you type "Introduction to MCMC" in a search engine you will be hit by almost $10$ freely downlodable .pdf files (written by academics and for educational purposes in their respective universities). I would suggest to examine every one of them, and check for level/style that suits you. It does not need necessarily to be a published book.
For GeneralizedLinearModels,
Dobson, A. J. (2002). An introduction to generalized linear models (2nd ed). CRC press.
is, I believe, a good (and tested) choice, and has topics relevant to, and some examples directly related to, the insurance field (shouldn't you also go into Extreme Value Theory though?). From the introduction:
The original purpose of the book was to present a unified theoretical
and conceptual framework for statistical modelling in a way that was
accessible to undergraduate students and researchers in other fields.
and
There is an emphasis on graphical methods for exploratory data
analysis, visualizing numerical optimization (for example, of the
likelihood function) and plotting residuals to check the adequacy of
models.
Contents
1 Introduction
1.1 Background
1.2 Scope
1.3 Notation
1.4 Distributions related to the Normal distribution
1.5 Quadratic forms
1.6 Estimation
1.7 Exercises
2 Model Fitting
2.1 Introduction
2.2 Examples
2.3 Some principles ofstatistica l modelling
2.4 Notation and coding for explanatory variables
2.5 Exercises
3 Exponential Family and Generalized Linear Models
3.1 Introduction
3.2 Exponential family of distributions
3.3 Properties ofdistribution s in the exponential family
3.4 Generalized linear models
3.5 Examples
3.6 Exercises
4 Estimation
4.1 Introduction
4.2 Example: Failure times for pressure vessels
4.3 Maximum likelihood estimation
4.4 Poisson regression example
4.5 Exercises
5 Inference
5.1 Introduction
5.2 Sampling distribution for score statistics
5.3 Taylor series approximations
5.4 Sampling distribution for maximum likelihood estimators
5.5 Log-likelihood ratio statistic
5.6 Sampling distribution for the deviance
5.7 Hypothesis testing
5.8 Exercises
6 Normal Linear Models
6.1 Introduction
6.2 Basic results
6.3 Multiple linear regression
6.4 Analysis of variance
6.5 Analysis ofc ovariance
6.6 General linear models
6.7 Exercises
7 Binary Variables and Logistic Regression
7.1 Probability distributions
7.2 Generalized linear models
7.3 Dose response models
7.4 General logistic regression model
7.5 Goodness offi t statistics
7.6 Residuals
7.7 Other diagnostics
7.8 Example: Senility and WAIS
7.9 Exercises
8 Nominal and Ordinal Logistic Regression
8.1 Introduction
8.2 Multinomial distribution
8.3 Nominal logistic regression
8.4 Ordinal logistic regression
8.5 General comments
8.6 Exercises
9 Count Data, Poisson Regression and Log-Linear Models
9.1 Introduction
9.2 Poisson regression
9.3 Examples ofco ntingency tables
9.4 Probability models for contingency tables
9.5 Log-linear models
9.6 Inference for log-linear models
9.7 Numerical examples
9.8 Remarks
9.9 Exercises
10 Survival Analysis
10.1 Introduction
10.2 Survivor functions and hazard functions
10.3 Empirical survivor function
10.4 Estimation
10.5 Inference
10.6 Model checking
10.7 Example: remission times
10.8 Exercises
11 Clustered and Longitudinal Data
11.1 Introduction
11.2 Example: Recovery from stroke
11.3 Repeated measures models for Normal data
11.4 Repeated measures models for non-Normal data
11.5 Multilevel models
11.6 Stroke example continued
11.7 Comments
11.8 Exercises
Software
References
